1 Preparations
1.1 Load data
# list filenames
file1_list <- list.files(file.path("data", "1"), pattern = "*.xlsx", full.names = TRUE)
file2_list <- list.files(file.path("data", "2"), pattern = "*.xlsx", full.names = TRUE)
# load data
df_raw_E1 <- sapply(file1_list, read_excel, na = "NA", simplify = FALSE) %>% bind_rows(.id = "id")
df_raw_E2 <- sapply(file2_list, read_excel, na = "NA", simplify = FALSE) %>% bind_rows(.id = "id")
# combine data from the two experiments
df_raw_E1_temp <- df_raw_E1 %>%
select(-c(SubTrial)) %>%
mutate(Probability = 0.5,
targetDuration = 200, # fix a bug in exp
Participant = Participant + 100)
df_raw_E2_temp <- df_raw_E2 %>%
select(-c(Age, Gender, Ethnicity, Block, FaceIndex)) %>%
mutate(Participant = Participant + 200,
Probability = if_else(grepl("75TopCue", Experiment), 0.75, 0.25))
df_raw <- bind_rows(df_raw_E1_temp, df_raw_E2_temp)
str(df_raw)## tibble[,22] [61,440 × 22] (S3: tbl_df/tbl/data.frame)
## $ id : chr [1:61440] "data/1/1_505_CF_Complete_Cue_2_2019-06-24-1519.xlsx" "data/1/1_505_CF_Complete_Cue_2_2019-06-24-1519.xlsx" "data/1/1_505_CF_Complete_Cue_2_2019-06-24-1519.xlsx" "data/1/1_505_CF_Complete_Cue_2_2019-06-24-1519.xlsx" ...
## $ Experiment : chr [1:61440] "109_cue" "109_cue" "109_cue" "109_cue" ...
## $ Participant : num [1:61440] 101 101 101 101 101 101 101 101 101 101 ...
## $ Trial : num [1:61440] 1 2 3 4 5 6 7 8 9 10 ...
## $ Condition : chr [1:61440] "Complete_cue" "Complete_cue" "Complete_cue" "Complete_cue" ...
## $ CuedHalf : chr [1:61440] "T" "T" "B" "B" ...
## $ Congruency : chr [1:61440] "I" "C" "I" "C" ...
## $ Alignment : chr [1:61440] "A" "M" "M" "M" ...
## $ SameDifferent : chr [1:61440] "S" "D" "D" "S" ...
## $ FaceGroup : chr [1:61440] "M5" "M1" "M3" "M1" ...
## $ StudyUpper : chr [1:61440] "M5116.png" "M1110.png" "M3174.png" "M1119.png" ...
## $ StudyLower : chr [1:61440] "M5185.png" "M1119.png" "M3138.png" "M1190.png" ...
## $ TargetUpper : chr [1:61440] "M5116.png" "M1190.png" "M3174.png" "M1119.png" ...
## $ TargetLower : chr [1:61440] "M5126.png" "M1173.png" "M3124.png" "M1190.png" ...
## $ thisResponse : chr [1:61440] "D" "D" "D" "D" ...
## $ isCorrect : num [1:61440] 0 1 1 0 1 1 1 1 1 1 ...
## $ reactionTime : num [1:61440] 0.755 0.634 1.311 0.999 1.376 ...
## $ studyDuration : num [1:61440] 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 ...
## $ targetDuration: num [1:61440] 200 200 200 200 200 200 200 200 200 200 ...
## $ maskDuration : num [1:61440] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...
## $ trialEndTime : chr [1:61440] "2019-06-24-15:20:04" "2019-06-24-15:20:07" "2019-06-24-15:20:11" "2019-06-24-15:20:15" ...
## $ Probability : num [1:61440] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...1.2 Tidy data
df_tidy <- df_raw %>%
filter(!is.na(thisResponse)) %>% # remove NA trials based on responses
mutate(Cue = if_else(CuedHalf == "T", "top", "bottom"),
Congruency = if_else(Congruency == "C", "congruent", "incongruent"),
Alignment = if_else(Alignment == "A", "aligned", "misaligned"),
SameDifferent = if_else(SameDifferent == "S", "same", "different"),
Participant = as_factor(Participant),
Cue = factor(Cue, levels = c("top", "bottom")),
Congruency = factor(Congruency, levels = c("congruent", "incongruent")),
Alignment = as_factor(Alignment),
SameDifferent = factor(SameDifferent, levels = c("same", "different")),
Probability = as_factor(Probability),
Resp = if_else(thisResponse == "S", 1, 0),
RT = round(reactionTime * 1000+200)) # plus the duration of target faces- Cue: top vs. bottom
- Congruency: congruent vs. incongruent
- Alignment: aligned vs. misaligned
- Identity (SameDifferent): same vs. different
Number of trials for each participant:
# Trial numbers in each condition
df_tidy %>%
group_by(Participant) %>%
summarize(nTotal = n()) ## # A tibble: 64 x 2
## Participant nTotal
## <fct> <int>
## 1 101 640
## 2 102 640
## 3 103 640
## 4 104 640
## 5 105 640
## 6 106 640
## 7 107 640
## 8 108 640
## 9 109 639
## 10 110 640
## # … with 54 more rows# For 3 participants in E1, one trail was removed due to no response recorded.# set successive difference coding for fixed effects
contrasts(df_tidy$Cue) <- MASS::contr.sdif(nlevels(df_tidy$Cue))
contrasts(df_tidy$Congruency) <- MASS::contr.sdif(nlevels(df_tidy$Congruency))
contrasts(df_tidy$Alignment) <- MASS::contr.sdif(nlevels(df_tidy$Alignment))
contrasts(df_tidy$SameDifferent) <- MASS::contr.sdif(nlevels(df_tidy$SameDifferent))
# set successive difference coding for random effects
df_lmm <- df_tidy %>%
mutate(
Cue_C = if_else(Cue == "top", -.5, .5),
Con_C = if_else(Congruency == "congruent", -.5, .5),
Ali_C = if_else(Alignment == "aligned", -.5, .5),
Sam_C = if_else(SameDifferent == "same", -.5, .5),
Cue_Con = Cue_C * Con_C,
Cue_Ali = Cue_C * Ali_C,
Cue_Sam = Cue_C * Sam_C,
Con_Ali = Con_C * Ali_C,
Con_Sam = Con_C * Sam_C,
Ali_Sam = Ali_C * Sam_C,
Cue_Con_Ali = Cue_Con * Ali_C,
Cue_Con_Sam = Cue_Con * Sam_C,
Cue_Ali_Sam = Cue_Ali * Sam_C,
Con_Ali_Sam = Con_Ali * Sam_C,
Cue_Con_Ali_Sam = Cue_Con_Ali * Sam_C
)
# save the data (for fitting model in cluster)
# save(df_lmm, file = file.path("data", "df_lmm.RData"))1.3 Steps to obtain the optimal model
- If the maximal model did not converge, correlations between random effects were removed, making the zero-correlation-parameter (ZCP) model.
- Principal component analysis implemented with “rePCA()” function was then used to identify random effects that explained less than 0.1% of the total variances; they were removed from the ZCP model to make the reduced model.
- The extended model was built by adding back the correlations between random effects in the reduced model.
- If the extended model did not converge, the random effects that explained less than 1% of total variances were identified by “rePCA()” and removed to make the updated extended model; this step was iterated until an extended model converged.
- The converged extended model was then compared to the reduced model via “anova()” function and the model that explained the data better (with smaller Bayesian Information Criterion) was used as the optimal model.
- All follow-up analyses were performed on the optimal model.
2 Experiment 1
df_lmm_E1 <- df_lmm %>%
filter(Experiment == "109_cue") %>%
droplevels()
# save(df_lmm_E1, file = file.path("data", "df_lmm_E1.RData"))There were 32 participants in Experiment 1.
2.1 Response (d’)
2.1.1 Fitting the generalized mixed models
2.1.1.1 The maximal model
# file_E1_resp_max <- file.path(folder_lmm, "E1_Resp_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_E1_resp_max)) {
# glmm_E1_resp_max <- glmer(
# Resp ~ Cue * Congruency * Alignment * SameDifferent +
# (Cue * Congruency * Alignment * SameDifferent | Participant), # Con_Ali_Sam
# family = binomial(link = "probit"),
# data = df_lmm_E1,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_E1_resp_max, file = file_E1_resp_max)
# } else {
# load(file_E1_resp_max)
# }
#
# print(summary(glmm_E1_resp_max), corr = FALSE)2.1.1.2 The zero-correlation-parameter model
file_E1_resp_zcp <- file.path(folder_lmm, "E1_Resp_lmm_zcp.RData")
# fit the zcp model
if (!file.exists(file_E1_resp_zcp)) {
glmm_E1_resp_zcp <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(Cue_C + Con_C + Ali_C + Sam_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam +
Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam || Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_zcp, file = file_E1_resp_zcp)
} else {
load(file_E1_resp_zcp)
}
print(summary(glmm_E1_resp_zcp), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam + Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 21936.9 22190.5 -10936.4 21872.9 20445
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.9358 -0.6657 0.2593 0.6445 4.4998
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 6.780e-02 0.2603885
## Participant.1 Cue_C 1.182e-01 0.3438058
## Participant.2 Con_C 3.893e-03 0.0623954
## Participant.3 Ali_C 4.835e-02 0.2198965
## Participant.4 Sam_C 1.695e-01 0.4116669
## Participant.5 Cue_Con 1.529e-02 0.1236598
## Participant.6 Cue_Ali 5.308e-02 0.2303939
## Participant.7 Cue_Sam 9.290e-01 0.9638497
## Participant.8 Con_Ali 0.000e+00 0.0000000
## Participant.9 Con_Sam 3.227e-01 0.5680713
## Participant.10 Ali_Sam 1.166e-10 0.0000108
## Participant.11 Cue_Con_Ali 0.000e+00 0.0000000
## Participant.12 Cue_Con_Sam 1.410e+00 1.1875858
## Participant.13 Cue_Ali_Sam 2.330e-02 0.1526353
## Participant.14 Con_Ali_Sam 1.291e-01 0.3593150
## Participant.15 Cue_Con_Ali_Sam 7.504e-02 0.2739304
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.37684 0.10414 13.221 < 2e-16 ***
## Cuebottom -0.27090 0.13817 -1.961 0.04993 *
## Congruencyincongruent -1.12419 0.09948 -11.300 < 2e-16 ***
## Alignmentmisaligned -0.13601 0.08431 -1.613 0.10672
## SameDifferentdifferent -2.33178 0.15088 -15.454 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.33173 0.13835 2.398 0.01650 *
## Cuebottom:Alignmentmisaligned -0.07531 0.10289 -0.732 0.46421
## Congruencyincongruent:Alignmentmisaligned 0.68120 0.09558 7.127 1.02e-12 ***
## Cuebottom:SameDifferentdifferent 0.69963 0.22026 3.176 0.00149 **
## Congruencyincongruent:SameDifferentdifferent 1.71693 0.17217 9.972 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.44037 0.09795 4.496 6.93e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.35334 0.12287 -2.876 0.00403 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.60078 0.24143 -2.488 0.01283 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13801 0.12738 -1.083 0.27860
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.00373 0.13725 -7.313 2.60e-13 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.72732 0.16944 4.292 1.77e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular2.1.1.3 The reduced model
summary(rePCA(glmm_E1_resp_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
## Standard deviation 1.188 0.9638 0.56807 0.41167 0.35932 0.34381 0.2739 0.26039 0.23039 0.21990 0.15264 0.12366 0.06240 1.08e-05 0 0
## Proportion of Variance 0.419 0.2760 0.09588 0.05035 0.03836 0.03512 0.0223 0.02015 0.01577 0.01437 0.00692 0.00454 0.00116 0.00e+00 0 0
## Cumulative Proportion 0.419 0.6951 0.79096 0.84132 0.87968 0.91480 0.9371 0.95724 0.97301 0.98738 0.99430 0.99884 1.00000 1.00e+00 1 1Con_Ali, Cue_Con_Ali, Ali_Sam, and Con_C were removed from extended model (glmm_E1_resp_zcp) due to that the variances they explained were smaller than 0.1%, making glmm_resp_rdc.
file_E1_resp_rdc <- file.path(folder_lmm, "E1_Resp_lmm_rdc.RData")
# fit the rdc model
if (!file.exists(file_E1_resp_rdc)) {
glmm_E1_resp_rdc <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(Cue_C + Ali_C + Sam_C + # Con_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam +
Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + # Cue_Con_Ali +
Cue_Con_Ali_Sam || Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_rdc, file = file_E1_resp_rdc)
} else {
load(file_E1_resp_rdc)
}
print(summary(glmm_E1_resp_rdc), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (Cue_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 21930 22152 -10937 21874 20449
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.5380 -0.6704 0.2629 0.6465 4.5875
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.06765 0.2601
## Participant.1 Cue_C 0.11821 0.3438
## Participant.2 Ali_C 0.04840 0.2200
## Participant.3 Sam_C 0.16847 0.4104
## Participant.4 Cue_Con 0.01592 0.1262
## Participant.5 Cue_Ali 0.05315 0.2305
## Participant.6 Cue_Sam 0.92706 0.9628
## Participant.7 Con_Sam 0.32072 0.5663
## Participant.8 Cue_Con_Sam 1.41750 1.1906
## Participant.9 Cue_Ali_Sam 0.02354 0.1534
## Participant.10 Con_Ali_Sam 0.13059 0.3614
## Participant.11 Cue_Con_Ali_Sam 0.07928 0.2816
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.37285 0.10391 13.212 < 2e-16 ***
## Cuebottom -0.26880 0.13829 -1.944 0.05193 .
## Congruencyincongruent -1.12002 0.09891 -11.324 < 2e-16 ***
## Alignmentmisaligned -0.13554 0.08433 -1.607 0.10800
## SameDifferentdifferent -2.32926 0.15105 -15.420 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.32913 0.13879 2.372 0.01771 *
## Cuebottom:Alignmentmisaligned -0.07570 0.10295 -0.735 0.46213
## Congruencyincongruent:Alignmentmisaligned 0.68092 0.09577 7.110 1.16e-12 ***
## Cuebottom:SameDifferentdifferent 0.69963 0.22074 3.169 0.00153 **
## Congruencyincongruent:SameDifferentdifferent 1.71425 0.17253 9.936 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.44093 0.09818 4.491 7.10e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.35335 0.12315 -2.869 0.00411 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.60079 0.24243 -2.478 0.01320 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13815 0.12770 -1.082 0.27932
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.00409 0.13778 -7.288 3.15e-13 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.72745 0.17016 4.275 1.91e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12.1.1.4 The extended model
file_E1_resp_etd <- file.path(folder_lmm, "E1_Resp_lmm_etd.RData")
# fit the etd model
if (!file.exists(file_E1_resp_etd)) {
glmm_E1_resp_etd <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(Cue_C + Ali_C + Sam_C + # Con_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam +
Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + # Cue_Con_Ali +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd, file = file_E1_resp_etd)
} else {
load(file_E1_resp_etd)
}
print(summary(glmm_E1_resp_etd), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (Cue_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 21953.0 22698.1 -10882.5 21765.0 20383
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.2143 -0.6713 0.2414 0.6543 5.2009
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.06913 0.2629
## Cue_C 0.11737 0.3426 -0.04
## Ali_C 0.04882 0.2210 0.00 0.11
## Sam_C 0.17347 0.4165 -0.03 -0.23 -0.31
## Cue_Con 0.03555 0.1885 0.03 0.19 -0.04 0.18
## Cue_Ali 0.05718 0.2391 -0.24 -0.09 -0.06 0.10 0.11
## Cue_Sam 0.92879 0.9637 0.45 0.17 0.30 -0.31 -0.67 -0.38
## Con_Sam 0.33820 0.5815 -0.15 0.02 0.03 -0.36 0.21 0.43 -0.23
## Cue_Con_Sam 1.51583 1.2312 0.15 0.00 0.37 -0.06 -0.68 -0.39 0.68 0.02
## Cue_Ali_Sam 0.11897 0.3449 0.12 0.02 -0.11 -0.42 -0.75 -0.60 0.65 -0.09 0.67
## Con_Ali_Sam 0.14149 0.3762 0.30 -0.11 -0.50 0.23 -0.65 -0.37 0.40 -0.49 0.41 0.66
## Cue_Con_Ali_Sam 0.41604 0.6450 0.28 0.10 0.08 -0.42 0.27 -0.03 0.27 0.02 -0.41 -0.13 -0.41
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.37921 0.10376 13.292 < 2e-16 ***
## Cuebottom -0.27976 0.11136 -2.512 0.011997 *
## Congruencyincongruent -1.12484 0.12260 -9.175 < 2e-16 ***
## Alignmentmisaligned -0.14692 0.09122 -1.611 0.107261
## SameDifferentdifferent -2.34239 0.15515 -15.097 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.34124 0.17196 1.984 0.047214 *
## Cuebottom:Alignmentmisaligned -0.06366 0.11998 -0.531 0.595732
## Congruencyincongruent:Alignmentmisaligned 0.71541 0.10524 6.798 1.06e-11 ***
## Cuebottom:SameDifferentdifferent 0.71000 0.17087 4.155 3.25e-05 ***
## Congruencyincongruent:SameDifferentdifferent 1.72964 0.20291 8.524 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.45760 0.11811 3.874 0.000107 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.38787 0.13556 -2.861 0.004221 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.61307 0.27336 -2.243 0.024914 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.14414 0.15375 -0.937 0.348512
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.04984 0.15962 -6.577 4.80e-11 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.75802 0.20051 3.781 0.000156 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_resp_etd))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## Standard deviation 1.4977 0.8779 0.6733 0.39416 0.35799 0.31452 0.25116 0.21968 0.0003291 4.271e-06 1.554e-07 0
## Proportion of Variance 0.5663 0.1946 0.1145 0.03923 0.03236 0.02498 0.01593 0.01218 0.0000000 0.000e+00 0.000e+00 0
## Cumulative Proportion 0.5663 0.7609 0.8753 0.91456 0.94691 0.97189 0.98782 1.00000 1.0000000 1.000e+00 1.000e+00 1Cue_Con, Ali_C, Cue_Ali, and Intercept were removed from the extended model.
file_E1_resp_etd1 <- file.path(folder_lmm, "E1_Resp_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_E1_resp_etd1)) {
glmm_E1_resp_etd1 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(0 + Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali +
Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + # Cue_Con_Ali +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd1, file = file_E1_resp_etd1)
} else {
load(file_E1_resp_etd1)
}
print(summary(glmm_E1_resp_etd1), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Cue_C + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 22521.5 22933.7 -11208.8 22417.5 20425
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.8285 -0.6903 0.2899 0.6800 4.5189
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_C 0.10766 0.3281
## Sam_C 0.16290 0.4036 -0.33
## Cue_Sam 0.81035 0.9002 0.26 -0.27
## Con_Sam 0.31546 0.5617 0.02 -0.40 -0.24
## Cue_Con_Sam 1.33283 1.1545 0.00 -0.01 0.65 0.06
## Cue_Ali_Sam 0.06888 0.2625 0.02 -0.42 0.67 -0.05 0.74
## Con_Ali_Sam 0.16811 0.4100 -0.12 0.28 0.42 -0.50 0.42 0.63
## Cue_Con_Ali_Sam 0.36562 0.6047 0.20 -0.45 0.27 -0.01 -0.47 -0.26 -0.40
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.30526 0.08039 16.236 < 2e-16 ***
## Cuebottom -0.21219 0.10068 -2.108 0.0351 *
## Congruencyincongruent -1.07631 0.10762 -10.001 < 2e-16 ***
## Alignmentmisaligned -0.14998 0.07570 -1.981 0.0476 *
## SameDifferentdifferent -2.24075 0.15104 -14.836 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.28714 0.14475 1.984 0.0473 *
## Cuebottom:Alignmentmisaligned -0.07573 0.09926 -0.763 0.4455
## Congruencyincongruent:Alignmentmisaligned 0.67370 0.10185 6.615 3.72e-11 ***
## Cuebottom:SameDifferentdifferent 0.65403 0.16618 3.936 8.30e-05 ***
## Congruencyincongruent:SameDifferentdifferent 1.66402 0.19578 8.500 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.44771 0.11329 3.952 7.75e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.31669 0.12997 -2.437 0.0148 *
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.56755 0.26167 -2.169 0.0301 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13430 0.14522 -0.925 0.3551
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.00715 0.15898 -6.335 2.37e-10 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.70048 0.19374 3.616 0.0003 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_resp_etd1))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## Standard deviation 1.3825 0.8423 0.6617 0.33736 0.31331 0.24743 3.564e-06 2.023e-07
## Proportion of Variance 0.5737 0.2129 0.1314 0.03416 0.02946 0.01838 0.000e+00 0.000e+00
## Cumulative Proportion 0.5737 0.7866 0.9180 0.95216 0.98162 1.00000 1.000e+00 1.000e+00Cue_Ali_Sam, and Cue_C were removed from extended1 model.
file_E1_resp_etd2 <- file.path(folder_lmm, "E1_Resp_lmm_etd2.RData")
# fit the etd2 model
if (!file.exists(file_E1_resp_etd2)) {
glmm_E1_resp_etd2 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(0 + Sam_C + # Con_C + Ali_C + Cue_C +
Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali +
Cue_Con_Sam + Con_Ali_Sam + # Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd2, file = file_E1_resp_etd2)
} else {
load(file_E1_resp_etd2)
}
print(summary(glmm_E1_resp_etd2), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 22716.3 23009.6 -11321.1 22642.3 20440
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.7939 -0.7181 0.2875 0.6817 4.2680
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Sam_C 0.1618 0.4022
## Cue_Sam 0.8394 0.9162 -0.30
## Con_Sam 0.3131 0.5595 -0.41 -0.23
## Cue_Con_Sam 1.2878 1.1348 0.02 0.62 0.06
## Con_Ali_Sam 0.1478 0.3845 0.33 0.41 -0.53 0.45
## Cue_Con_Ali_Sam 0.3708 0.6090 -0.54 0.36 0.01 -0.43 -0.40
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.31967 0.08665 15.231 < 2e-16 ***
## Cuebottom -0.24504 0.09985 -2.454 0.014127 *
## Congruencyincongruent -1.08920 0.10640 -10.237 < 2e-16 ***
## Alignmentmisaligned -0.16465 0.07168 -2.297 0.021627 *
## SameDifferentdifferent -2.23527 0.15677 -14.258 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.31331 0.14175 2.210 0.027084 *
## Cuebottom:Alignmentmisaligned -0.05537 0.09373 -0.591 0.554748
## Congruencyincongruent:Alignmentmisaligned 0.68730 0.10048 6.840 7.93e-12 ***
## Cuebottom:SameDifferentdifferent 0.67090 0.17333 3.871 0.000109 ***
## Congruencyincongruent:SameDifferentdifferent 1.66461 0.19293 8.628 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.46067 0.10223 4.506 6.60e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.33808 0.12902 -2.620 0.008786 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.58192 0.25547 -2.278 0.022737 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.15227 0.13083 -1.164 0.244449
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.01599 0.15525 -6.544 5.98e-11 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.71534 0.19209 3.724 0.000196 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_resp_etd2))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6]
## Standard deviation 1.3421 0.8715 0.6570 0.26879 0.23697 3.02e-07
## Proportion of Variance 0.5772 0.2434 0.1383 0.02315 0.01799 0.00e+00
## Cumulative Proportion 0.5772 0.8205 0.9588 0.98201 1.00000 1.00e+00Con_Ali_Sam was removed from extended2 model.
file_E1_resp_etd3 <- file.path(folder_lmm, "E1_Resp_lmm_etd3.RData")
# fit the etd3 model
if (!file.exists(file_E1_resp_etd3)) {
glmm_E1_resp_etd3 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(0 + Sam_C + # Con_C + Ali_C + Cue_C +
Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd3, file = file_E1_resp_etd3)
} else {
load(file_E1_resp_etd3)
}
print(summary(glmm_E1_resp_etd3), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 22717.1 22962.8 -11327.5 22655.1 20446
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.9575 -0.7151 0.2997 0.6853 3.8068
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Sam_C 0.1599 0.3998
## Cue_Sam 0.8401 0.9166 -0.30
## Con_Sam 0.3070 0.5541 -0.41 -0.22
## Cue_Con_Sam 1.2733 1.1284 0.01 0.62 0.07
## Cue_Con_Ali_Sam 0.3498 0.5914 -0.55 0.39 -0.02 -0.43
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.31216 0.08357 15.701 < 2e-16 ***
## Cuebottom -0.24399 0.09983 -2.444 0.014521 *
## Congruencyincongruent -1.08313 0.09483 -11.422 < 2e-16 ***
## Alignmentmisaligned -0.15610 0.06780 -2.302 0.021308 *
## SameDifferentdifferent -2.22155 0.15012 -14.799 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.31497 0.14097 2.234 0.025466 *
## Cuebottom:Alignmentmisaligned -0.05378 0.09324 -0.577 0.564069
## Congruencyincongruent:Alignmentmisaligned 0.68213 0.08994 7.584 3.35e-14 ***
## Cuebottom:SameDifferentdifferent 0.66779 0.17350 3.849 0.000119 ***
## Congruencyincongruent:SameDifferentdifferent 1.65395 0.16723 9.890 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.44496 0.09150 4.863 1.15e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.34682 0.12811 -2.707 0.006786 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.58436 0.25391 -2.301 0.021366 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.15320 0.12967 -1.181 0.237425
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.00568 0.12728 -7.901 2.76e-15 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.72743 0.18994 3.830 0.000128 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_resp_etd3))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5]
## Standard deviation 1.3208 0.8690 0.6068 0.24931 0
## Proportion of Variance 0.5954 0.2577 0.1257 0.02121 0
## Cumulative Proportion 0.5954 0.8531 0.9788 1.00000 1Sam_C was removed from extended3 model.
file_E1_resp_etd4 <- file.path(folder_lmm, "E1_Resp_lmm_etd4.RData")
# fit the etd4 model
if (!file.exists(file_E1_resp_etd4)) {
glmm_E1_resp_etd4 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd4, file = file_E1_resp_etd4)
} else {
load(file_E1_resp_etd4)
}
print(summary(glmm_E1_resp_etd4), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 23054.2 23260.3 -11501.1 23002.2 20451
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7093 -0.7045 0.3406 0.6959 2.6843
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.7870 0.8871
## Con_Sam 0.2681 0.5178 -0.27
## Cue_Con_Sam 1.2556 1.1205 0.66 0.08
## Cue_Con_Ali_Sam 0.3112 0.5579 0.35 -0.05 -0.42
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.25684 0.05822 21.589 < 2e-16 ***
## Cuebottom -0.20869 0.09448 -2.209 0.027191 *
## Congruencyincongruent -1.03225 0.09143 -11.290 < 2e-16 ***
## Alignmentmisaligned -0.14259 0.06604 -2.159 0.030847 *
## SameDifferentdifferent -2.12265 0.09192 -23.092 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.28160 0.13858 2.032 0.042146 *
## Cuebottom:Alignmentmisaligned -0.06807 0.09092 -0.749 0.454019
## Congruencyincongruent:Alignmentmisaligned 0.65469 0.08791 7.447 9.53e-14 ***
## Cuebottom:SameDifferentdifferent 0.59888 0.16245 3.687 0.000227 ***
## Congruencyincongruent:SameDifferentdifferent 1.56822 0.16045 9.774 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.41327 0.08877 4.656 3.23e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.31889 0.12506 -2.550 0.010777 *
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.52439 0.24958 -2.101 0.035634 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.12332 0.12589 -0.980 0.327267
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.95849 0.12374 -7.746 9.48e-15 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.68209 0.18425 3.702 0.000214 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_resp_etd4))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4]
## Standard deviation 1.3142 0.7964 0.5105 1.346e-07
## Proportion of Variance 0.6587 0.2419 0.0994 0.000e+00
## Cumulative Proportion 0.6587 0.9006 1.0000 1.000e+00Con_Sam was removed from extended4 model.
file_E1_resp_etd5 <- file.path(folder_lmm, "E1_Resp_lmm_etd5.RData")
# fit the etd5 model
if (!file.exists(file_E1_resp_etd5)) {
glmm_E1_resp_etd5 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali + Con_Sam +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm_E1,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_resp_etd5, file = file_E1_resp_etd5)
} else {
load(file_E1_resp_etd5)
}
print(summary(glmm_E1_resp_etd5), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Cue_Sam + Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 23165.7 23340.1 -11560.8 23121.7 20455
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4835 -0.7183 0.3488 0.7120 2.9989
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.8046 0.897
## Cue_Con_Sam 1.3785 1.174 0.63
## Cue_Con_Ali_Sam 0.2820 0.531 0.42 -0.45
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.25396 0.05981 20.964 < 2e-16 ***
## Cuebottom -0.22198 0.09690 -2.291 0.021974 *
## Congruencyincongruent -1.02711 0.08340 -12.316 < 2e-16 ***
## Alignmentmisaligned -0.13955 0.06595 -2.116 0.034355 *
## SameDifferentdifferent -2.11838 0.09607 -22.050 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.29631 0.14241 2.081 0.037468 *
## Cuebottom:Alignmentmisaligned -0.06778 0.09040 -0.750 0.453416
## Congruencyincongruent:Alignmentmisaligned 0.64489 0.08754 7.367 1.75e-13 ***
## Cuebottom:SameDifferentdifferent 0.61898 0.16834 3.677 0.000236 ***
## Congruencyincongruent:SameDifferentdifferent 1.55875 0.14196 10.980 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.40915 0.08855 4.621 3.82e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.31001 0.12406 -2.499 0.012461 *
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.54738 0.25822 -2.120 0.034021 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.12365 0.12482 -0.991 0.321859
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.94527 0.12291 -7.691 1.46e-14 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.67025 0.18186 3.686 0.000228 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular2.1.1.5 The optimal model
# compare the extended and reduced model
anova(glmm_E1_resp_etd5, glmm_E1_resp_rdc, refit = FALSE)## Data: df_lmm_E1
## Models:
## glmm_E1_resp_etd5: Resp ~ Cue * Congruency * Alignment * SameDifferent + (0 + Cue_Sam +
## glmm_E1_resp_etd5: Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## glmm_E1_resp_rdc: Resp ~ Cue * Congruency * Alignment * SameDifferent + (Cue_C +
## glmm_E1_resp_rdc: Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam +
## glmm_E1_resp_rdc: Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_E1_resp_etd5 22 23166 23340 -11561 23122
## glmm_E1_resp_rdc 28 21930 22152 -10937 21874 1247.6 6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to BIC, the reduced model (glmm_resp_rdc) explained the data better than the extended model (glmm_resp_etd5) and, therefore, the reduced model is used as the optimal model.
glmm_E1_resp_opt <- glmm_E1_resp_rdc
print(summary(glmm_E1_resp_opt), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + (Cue_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm_E1
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 21930 22152 -10937 21874 20449
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.5380 -0.6704 0.2629 0.6465 4.5875
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.06765 0.2601
## Participant.1 Cue_C 0.11821 0.3438
## Participant.2 Ali_C 0.04840 0.2200
## Participant.3 Sam_C 0.16847 0.4104
## Participant.4 Cue_Con 0.01592 0.1262
## Participant.5 Cue_Ali 0.05315 0.2305
## Participant.6 Cue_Sam 0.92706 0.9628
## Participant.7 Con_Sam 0.32072 0.5663
## Participant.8 Cue_Con_Sam 1.41750 1.1906
## Participant.9 Cue_Ali_Sam 0.02354 0.1534
## Participant.10 Con_Ali_Sam 0.13059 0.3614
## Participant.11 Cue_Con_Ali_Sam 0.07928 0.2816
## Number of obs: 20477, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.37285 0.10391 13.212 < 2e-16 ***
## Cuebottom -0.26880 0.13829 -1.944 0.05193 .
## Congruencyincongruent -1.12002 0.09891 -11.324 < 2e-16 ***
## Alignmentmisaligned -0.13554 0.08433 -1.607 0.10800
## SameDifferentdifferent -2.32926 0.15105 -15.420 < 2e-16 ***
## Cuebottom:Congruencyincongruent 0.32913 0.13879 2.372 0.01771 *
## Cuebottom:Alignmentmisaligned -0.07570 0.10295 -0.735 0.46213
## Congruencyincongruent:Alignmentmisaligned 0.68092 0.09577 7.110 1.16e-12 ***
## Cuebottom:SameDifferentdifferent 0.69963 0.22074 3.169 0.00153 **
## Congruencyincongruent:SameDifferentdifferent 1.71425 0.17253 9.936 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.44093 0.09818 4.491 7.10e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.35335 0.12315 -2.869 0.00411 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.60079 0.24243 -2.478 0.01320 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13815 0.12770 -1.082 0.27932
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -1.00409 0.13778 -7.288 3.15e-13 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.72745 0.17016 4.275 1.91e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12.1.2 Estimated marginal means
2.1.2.1 Estimated marginal means for hit and false alarm
(emm_E1_resp <- emmeans(glmm_E1_resp_opt, ~ Alignment + Congruency + Cue + SameDifferent))## Alignment Congruency Cue SameDifferent emmean SE df asymp.LCL asymp.UCL
## aligned congruent top same 1.3728 0.1039 Inf 1.1692 1.5765
## misaligned congruent top same 1.2373 0.1023 Inf 1.0367 1.4379
## aligned incongruent top same 0.2528 0.0976 Inf 0.0615 0.4441
## misaligned incongruent top same 0.7982 0.0996 Inf 0.6030 0.9934
## aligned congruent bottom same 1.1040 0.1007 Inf 0.9066 1.3015
## misaligned congruent bottom same 0.8928 0.0992 Inf 0.6983 1.0873
## aligned incongruent bottom same 0.3132 0.0973 Inf 0.1224 0.5039
## misaligned incongruent bottom same 0.4295 0.0975 Inf 0.2384 0.6206
## aligned congruent top different -0.9564 0.1000 Inf -1.1524 -0.7605
## misaligned congruent top different -0.6510 0.0983 Inf -0.8436 -0.4585
## aligned incongruent top different -0.3622 0.0977 Inf -0.5537 -0.1706
## misaligned incongruent top different -0.3800 0.0975 Inf -0.5710 -0.1889
## aligned congruent bottom different -0.5256 0.0980 Inf -0.7177 -0.3334
## misaligned congruent bottom different -0.4340 0.0976 Inf -0.6254 -0.2427
## aligned incongruent bottom different -0.2030 0.0973 Inf -0.3937 -0.0123
## misaligned incongruent bottom different -0.0605 0.0972 Inf -0.2511 0.1300
##
## Results are given on the probit (not the response) scale.
## Confidence level used: 0.952.1.2.2 Estimated marginal means for d’
emm_E1_d <- contrast(emm_E1_resp, method = "pairwise", simple = "SameDifferent")
summary(emm_E1_d[1:8], infer = c(TRUE, FALSE), adjust = "none")## contrast Alignment Congruency Cue estimate SE df asymp.LCL asymp.UCL
## same - different aligned congruent top 2.329 0.151 Inf 2.033 2.625
## same - different misaligned congruent top 1.888 0.149 Inf 1.597 2.180
## same - different aligned incongruent top 0.615 0.145 Inf 0.331 0.899
## same - different misaligned incongruent top 1.178 0.146 Inf 0.892 1.465
## same - different aligned congruent bottom 1.630 0.147 Inf 1.341 1.919
## same - different misaligned congruent bottom 1.327 0.146 Inf 1.040 1.613
## same - different aligned incongruent bottom 0.516 0.145 Inf 0.233 0.800
## same - different misaligned incongruent bottom 0.490 0.145 Inf 0.207 0.774
##
## Note: contrasts are still on the probit scale
## Confidence level used: 0.95# quick check (uncorrected)
# emmip(emm_E1_d, Congruency ~ Alignment | Cue, CIs = TRUE) plot_E1_cf_d <- summary(emm_E1_d[1:8], infer = c(TRUE, FALSE), adjust = "sidak") %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(. ~Cue, switch = "both") +
coord_cartesian(ylim = ylimit_cf_d) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = expression("Sensitivity"~italic("d'")), fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("***", "", "", "", "*", "", "", ""), color = "red", size = 6, nudge_y = 0.5, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E1_cf_d.pdf", plot_E1_cf_d, width = 8, height = 4.8)
plot_E1_cf_d
# ggsave(filename = "E1_cf_d.pdf",
# plot_E1_cf_d +
# theme(legend.position=c(0.5, 0.15)),
# width = 7)2.1.2.3 Composite effects
Composite face effects for top and bottom parts:
emm_E1_d_cf <- contrast(emm_E1_resp, interaction = "pairwise", by = "Cue")
summary(emm_E1_d_cf[1:2], infer = TRUE)## Alignment_pairwise Congruency_pairwise SameDifferent_pairwise Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned congruent - incongruent same - different top 1.004 0.138 Inf 0.734 1.274 7.288 <.0001
## aligned - misaligned congruent - incongruent same - different bottom 0.277 0.130 Inf 0.022 0.531 2.129 0.0333
##
## Confidence level used: 0.95emm_E1_d_con <- contrast(emm_E1_resp, interaction = "pairwise", by = c("Cue", "Alignment"))
summary(emm_E1_d_con[c(1,3)], infer = TRUE)## Congruency_pairwise SameDifferent_pairwise Cue Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent same - different top aligned 1.71 0.173 Inf 1.376 2.05 9.936 <.0001
## congruent - incongruent same - different bottom aligned 1.11 0.169 Inf 0.782 1.44 6.583 <.0001
##
## Confidence level used: 0.952.1.2.4 Facilitation and interference
# Sensitivity d'
emm_E1_d_fi <- contrast(emm_E1_resp, interaction = "pairwise", by = c("Cue", "Congruency"), adjust = "sidak")
summary(emm_E1_d_fi[1:4], infer=TRUE)## Alignment_pairwise SameDifferent_pairwise Cue Congruency estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned same - different top congruent 0.4409 0.0982 Inf 0.1964 0.685 4.491 <.0001
## aligned - misaligned same - different top incongruent -0.5632 0.0862 Inf -0.7778 -0.349 -6.536 <.0001
## aligned - misaligned same - different bottom congruent 0.3028 0.0897 Inf 0.0794 0.526 3.376 0.0029
## aligned - misaligned same - different bottom incongruent 0.0261 0.0830 Inf -0.1807 0.233 0.315 0.9963
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 4 estimates
## P value adjustment: sidak method for 4 tests# # showing the differences between aligned and misaligned (aligned-misaligned)
# emmip(emm_E1_d_fi[1:4], ~ Cue | Congruency, CIs = TRUE, adjust = "sidak") +
# geom_hline(yintercept = 0, linetype = "dashed")plot_E1_cffi_d <- summary(emm_E1_d_fi[1:4], infer=TRUE, adjust = "sidak") %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(. ~ Congruency, switch = "both") +
coord_cartesian(ylim = ylimit_cf_fi_d) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(italic("d'")~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E1_fi_d.pdf", plot_E1_cffi_d, width = 7, height = 4.55)
plot_E1_cffi_d
plot_E1_cf_d_ <- plot_E1_cf_d +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.6, 0.075),
legend.box = "horizontal")
plot_E1_d <- ggarrange(plot_E1_cf_d_, plot_E1_cffi_d,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E1_d.pdf", plot_E1_d, width = 10, height = 4.5)
plot_E1_d
2.1.2.5 Comparisons between facilitation and interference
contrast(emm_E1_d_fi, method = list("faci-inte"=c(1, 1)), by = "Cue")[1:2] %>%
summary(infer = TRUE)## contrast Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top -0.122 0.123 Inf -0.363 0.119 -0.993 0.3206
## faci-inte bottom 0.329 0.114 Inf 0.106 0.552 2.886 0.0039
##
## Confidence level used: 0.952.2 Response times
df_lmm_E1_rt <- df_lmm_E1 %>%
filter(isCorrect == 1)
# save(df_lmm_E1_rt, file = file.path("data", "df_lmm_E1_rt.RData"))2.2.1 Fitting the generalized mixed models
with log-transformation. #### The maximal model
# file_E1_rt_max <- file.path(folder_lmm, "E1_rt_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_E1_rt_max)) {
# glmm_E1_rt_max <- glmer(
# log(RT) ~ Cue * Congruency * Alignment +
# (Cue * Congruency * Alignment | Participant),
# family = lognormal(),
# data = df_lmm_rt,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_E1_rt_max, file = file_E1_rt_max)
# } else {
# load(file_E1_rt_max)
# }
#
# print(summary(glmm_E1_rt_max), corr = FALSE)2.2.1.1 The zero-correlation-parameter model
file_E1_rt_zcp <- file.path(folder_lmm, "E1_rt_lmm_zcp.RData")
# fit the zcp1 model
if (!file.exists(file_E1_rt_zcp)) {
glmm_E1_rt_zcp <- lmer(
log(RT) ~ Cue * Congruency * Alignment +
(Cue_C + Con_C + Ali_C +
Cue_Con + Cue_Ali + Con_Ali +
Cue_Con_Ali || Participant),
data = df_lmm_E1_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_rt_zcp, file = file_E1_rt_zcp)
} else {
load(file_E1_rt_zcp)
}
print(summary(glmm_E1_rt_zcp), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Con_Ali + Cue_Con_Ali || Participant)
## Data: df_lmm_E1_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 13677.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6186 -0.5735 -0.1346 0.4295 7.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0725762 0.26940
## Participant.1 Cue_C 0.0226908 0.15063
## Participant.2 Con_C 0.0010608 0.03257
## Participant.3 Ali_C 0.0011955 0.03458
## Participant.4 Cue_Con 0.0007338 0.02709
## Participant.5 Cue_Ali 0.0046874 0.06846
## Participant.6 Con_Ali 0.0000000 0.00000
## Participant.7 Cue_Con_Ali 0.0231449 0.15213
## Residual 0.1478702 0.38454
## Number of obs: 14339, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.689329 0.050535 38.630155 132.371 < 2e-16 ***
## Cuebottom 0.072469 0.030700 46.934968 2.361 0.022456 *
## Congruencyincongruent 0.060203 0.015862 110.775801 3.796 0.000241 ***
## Alignmentmisaligned 0.035569 0.016166 89.228593 2.200 0.030371 *
## Cuebottom:Congruencyincongruent 0.001602 0.023408 52.241192 0.068 0.945697
## Cuebottom:Alignmentmisaligned 0.015209 0.025040 47.196342 0.607 0.546497
## Congruencyincongruent:Alignmentmisaligned -0.039663 0.022484 56.766074 -1.764 0.083102 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.007022 0.037462 27.620253 -0.187 0.852689
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingular2.2.1.2 The reduced model
summary(rePCA(glmm_E1_rt_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## Standard deviation 0.7006 0.3956 0.3917 0.17804 0.08992 0.08470 0.07045 0
## Proportion of Variance 0.5756 0.1836 0.1800 0.03718 0.00948 0.00841 0.00582 0
## Cumulative Proportion 0.5756 0.7591 0.9391 0.97629 0.98577 0.99418 1.00000 1Con_Ali was removed from extended model (glmm_E1_rt_zcp) due to that the variance it explained was smaller than 0.1%, making glmm_E1_rt_rdc.
file_E1_rt_rdc <- file.path(folder_lmm, "E1_rt_lmm_rdc.RData")
# fit the rdc1 model
if (!file.exists(file_E1_rt_rdc)) {
glmm_E1_rt_rdc <- lmer(
log(RT) ~ Cue * Congruency * Alignment +
(Cue_C + Con_C + Ali_C +
Cue_Con + Cue_Ali + # Con_Ali +
Cue_Con_Ali || Participant),
data = df_lmm_E1_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_rt_rdc, file = file_E1_rt_rdc)
} else {
load(file_E1_rt_rdc)
}
print(summary(glmm_E1_rt_rdc), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Cue_Con_Ali || Participant)
## Data: df_lmm_E1_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 13677.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6186 -0.5735 -0.1346 0.4295 7.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0725764 0.26940
## Participant.1 Cue_C 0.0226910 0.15064
## Participant.2 Con_C 0.0010608 0.03257
## Participant.3 Ali_C 0.0011956 0.03458
## Participant.4 Cue_Con 0.0007337 0.02709
## Participant.5 Cue_Ali 0.0046876 0.06847
## Participant.6 Cue_Con_Ali 0.0231478 0.15214
## Residual 0.1478701 0.38454
## Number of obs: 14339, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.689329 0.050535 38.630041 132.371 < 2e-16 ***
## Cuebottom 0.072469 0.030701 46.934893 2.361 0.022456 *
## Congruencyincongruent 0.060203 0.015862 110.770723 3.796 0.000241 ***
## Alignmentmisaligned 0.035569 0.016166 89.225948 2.200 0.030373 *
## Cuebottom:Congruencyincongruent 0.001602 0.023409 52.237565 0.068 0.945701
## Cuebottom:Alignmentmisaligned 0.015209 0.025040 47.194938 0.607 0.546510
## Congruencyincongruent:Alignmentmisaligned -0.039663 0.022485 56.760997 -1.764 0.083108 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.007021 0.037463 27.618818 -0.187 0.852700
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12.2.1.3 The extended model
file_E1_rt_etd <- file.path(folder_lmm, "E1_rt_lmm_etd.RData")
# fit the etd1 model
if (!file.exists(file_E1_rt_etd)) {
glmm_E1_rt_etd <- lmer(
log(RT) ~ Cue * Congruency * Alignment +
(Cue_C + Con_C + Ali_C +
Cue_Con + Cue_Ali + # Con_Ali +
Cue_Con_Ali | Participant),
data = df_lmm_E1_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_rt_etd, file = file_E1_rt_etd)
} else {
load(file_E1_rt_etd)
}
print(summary(glmm_E1_rt_etd), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Cue_Con_Ali | Participant)
## Data: df_lmm_E1_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 13639.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7341 -0.5741 -0.1341 0.4281 7.5985
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.072195 0.26869
## Cue_C 0.022630 0.15043 -0.02
## Con_C 0.001094 0.03308 -0.40 0.19
## Ali_C 0.001456 0.03816 -0.30 -0.23 0.54
## Cue_Con 0.002246 0.04739 0.18 0.30 -0.10 -0.89
## Cue_Ali 0.005632 0.07505 -0.05 -0.01 -0.16 0.67 -0.91
## Cue_Con_Ali 0.027429 0.16562 -0.46 -0.25 -0.27 0.52 -0.79 0.82
## Residual 0.147687 0.38430
## Number of obs: 14339, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.6890097 0.0539790 31.1138223 123.919 < 2e-16 ***
## Cuebottom 0.0724021 0.0269948 31.6152685 2.682 0.01153 *
## Congruencyincongruent 0.0604124 0.0173550 44.2973201 3.481 0.00113 **
## Alignmentmisaligned 0.0361463 0.0139979 47.8768479 2.582 0.01293 *
## Cuebottom:Congruencyincongruent 0.0008654 0.0286328 30.2534505 0.030 0.97609
## Cuebottom:Alignmentmisaligned 0.0154113 0.0192267 39.4831241 0.802 0.42761
## Congruencyincongruent:Alignmentmisaligned -0.0397233 0.0231668 56.6025894 -1.715 0.09188 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.0058548 0.0391678 29.1435306 -0.149 0.88220
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E1_rt_etd))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## Standard deviation 0.7406 0.4537 0.3537 0.13699 0.01013 0.001418 7.519e-19
## Proportion of Variance 0.6106 0.2291 0.1393 0.02089 0.00011 0.000000 0.000e+00
## Cumulative Proportion 0.6106 0.8397 0.9790 0.99988 1.00000 1.000000 1.000e+00Con_C, Ali_C, and Cue_Con were removed from extended model.
file_E1_rt_etd1 <- file.path(folder_lmm, "E1_rt_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_E1_rt_etd1)) {
glmm_E1_rt_etd1 <- lmer(
log(RT) ~ Cue * Congruency * Alignment +
(Cue_C + # Con_C + Ali_C +
Cue_Ali + # Con_Ali + Cue_Con +
Cue_Con_Ali | Participant),
data = df_lmm_E1_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E1_rt_etd1, file = file_E1_rt_etd1)
} else {
load(file_E1_rt_etd1)
}
print(summary(glmm_E1_rt_etd1), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Cue_Ali + Cue_Con_Ali | Participant)
## Data: df_lmm_E1_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 13678.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7618 -0.5749 -0.1328 0.4291 7.6980
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.072713 0.26965
## Cue_C 0.022643 0.15048 -0.02
## Cue_Ali 0.004764 0.06902 -0.01 0.00
## Cue_Con_Ali 0.026729 0.16349 -0.43 -0.26 0.84
## Residual 0.148441 0.38528
## Number of obs: 14339, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.689159 0.051646 31.691272 129.520 < 2e-16 ***
## Cuebottom 0.071427 0.027748 33.934439 2.574 0.01459 *
## Congruencyincongruent 0.060875 0.014804 146.126193 4.112 6.52e-05 ***
## Alignmentmisaligned 0.035516 0.012534 87.573213 2.834 0.00571 **
## Cuebottom:Congruencyincongruent 0.002798 0.023482 58.492199 0.119 0.90557
## Cuebottom:Alignmentmisaligned 0.016498 0.018961 28.771290 0.870 0.39145
## Congruencyincongruent:Alignmentmisaligned -0.041767 0.023105 54.360420 -1.808 0.07618 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.007626 0.038908 27.563343 -0.196 0.84604
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12.2.1.4 The optimal model
# compare the extended and reduced model
anova(glmm_E1_rt_etd1, glmm_E1_rt_rdc, refit = FALSE)## Data: df_lmm_E1_rt
## Models:
## glmm_E1_rt_rdc: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Con_C + Ali_C +
## glmm_E1_rt_rdc: Cue_Con + Cue_Ali + Cue_Con_Ali || Participant)
## glmm_E1_rt_etd1: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Cue_Ali + Cue_Con_Ali |
## glmm_E1_rt_etd1: Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_E1_rt_rdc 16 13709 13830 -6838.6 13677
## glmm_E1_rt_etd1 19 13717 13861 -6839.5 13679 0 3 1According to BIC, the reduced model (glmm_E1_rt_rdc) explained the data better than the extended model (glmm_E1_rt_etd1) and, therefore, the reduced model is used as the optimal model.
glmm_E1_rt_opt <- glmm_E1_rt_rdc
print(summary(glmm_E1_rt_opt), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Cue_Con_Ali || Participant)
## Data: df_lmm_E1_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 13677.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6186 -0.5735 -0.1346 0.4295 7.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0725764 0.26940
## Participant.1 Cue_C 0.0226910 0.15064
## Participant.2 Con_C 0.0010608 0.03257
## Participant.3 Ali_C 0.0011956 0.03458
## Participant.4 Cue_Con 0.0007337 0.02709
## Participant.5 Cue_Ali 0.0046876 0.06847
## Participant.6 Cue_Con_Ali 0.0231478 0.15214
## Residual 0.1478701 0.38454
## Number of obs: 14339, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.689329 0.050535 38.630041 132.371 < 2e-16 ***
## Cuebottom 0.072469 0.030701 46.934893 2.361 0.022456 *
## Congruencyincongruent 0.060203 0.015862 110.770723 3.796 0.000241 ***
## Alignmentmisaligned 0.035569 0.016166 89.225948 2.200 0.030373 *
## Cuebottom:Congruencyincongruent 0.001602 0.023409 52.237565 0.068 0.945701
## Cuebottom:Alignmentmisaligned 0.015209 0.025040 47.194938 0.607 0.546510
## Congruencyincongruent:Alignmentmisaligned -0.039663 0.022485 56.760997 -1.764 0.083108 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.007021 0.037463 27.618818 -0.187 0.852700
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12.2.2 Estimated marginal means
2.2.2.1 Estimated marginal means for RT
file_E1_rt_emm <- file.path(folder_lmm, "E1_rt_emm.RData")
if (!file.exists(file_E1_rt_emm)) {
emm_E1_rt <- emmeans(glmm_E1_rt_opt, ~ Cue + Congruency + Alignment)
} else {
load(file_E1_rt_emm)
}
# emmip(regrid(emm_E1_rt), Congruency ~ Alignment | Cue, CIs = TRUE)
summary(emm_E1_rt, type = "response") # equivalent to regrid(emm_rt)## Cue Congruency Alignment response SE df asymp.LCL asymp.UCL
## top congruent aligned 804 40.6 Inf 728 887
## bottom congruent aligned 864 43.7 Inf 783 954
## top incongruent aligned 854 43.4 Inf 773 943
## bottom incongruent aligned 919 46.7 Inf 832 1016
## top congruent misaligned 833 42.1 Inf 754 920
## bottom congruent misaligned 909 46.1 Inf 823 1004
## top incongruent misaligned 850 43.1 Inf 770 939
## bottom incongruent misaligned 923 46.9 Inf 835 1020
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95
## Intervals are back-transformed from the log scaleplot_E1_cf_rt <- summary(emm_E1_rt, type = "response") %>%
as_tibble() %>%
ggplot(aes(y = response, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(. ~Cue, switch = "both") +
coord_cartesian(ylim = ylimit_cf_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = "Correct response times (ms)", fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("", "", "++", "+", "", "", "", ""), color = "blue", size = 6, nudge_y = 50, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E1_cf_rt.pdf", plot_E1_cf_rt, width = 8, height = 4.8)
plot_E1_cf_rt
2.2.2.2 Composite effects
Composite face effects for top and bottom parts:
emm_E1_rt_cf <- contrast(regrid(emm_E1_rt), interaction = "pairwise", by = "Cue", infer = TRUE)
emm_E1_rt_cf[1:2]## Congruency_pairwise Alignment_pairwise Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent aligned - misaligned top -32.6 18.9 Inf -69.6 4.424 -1.726 0.0844
## congruent - incongruent aligned - misaligned bottom -41.2 21.1 Inf -82.6 0.119 -1.954 0.0507
##
## Confidence level used: 0.95emm_E1_rt_con <- contrast(regrid(emm_E1_rt), interaction = "pairwise", by = c("Cue", "Alignment"))
summary(emm_E1_rt_con[c(1,2)], infer = TRUE)## Congruency_pairwise Cue Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent top aligned -49.9 13.4 Inf -76.2 -23.6 -3.715 0.0002
## congruent - incongruent bottom aligned -55.1 14.7 Inf -83.9 -26.3 -3.748 0.0002
##
## Confidence level used: 0.952.2.2.3 Facilitation and interference
emm_E1_rt_fi <- contrast(regrid(emm_E1_rt), "pairwise", by = c("Cue", "Congruency"), infer=TRUE, adjust = "sidak")
# emmip(emm_E1_rt_fi[1:4], ~ Cue | Congruency, CIs = TRUE, adjust = "sidak")
emm_E1_rt_fi[1:4]## contrast Cue Congruency estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned top congruent -29.10 13.3 Inf -62.3 4.06 -2.186 0.1103
## aligned - misaligned bottom congruent -45.02 14.9 Inf -82.2 -7.85 -3.017 0.0102
## aligned - misaligned top incongruent 3.49 14.8 Inf -33.4 40.38 0.236 0.9988
## aligned - misaligned bottom incongruent -3.77 16.5 Inf -44.8 37.22 -0.229 0.9989
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 4 estimates
## P value adjustment: sidak method for 4 testsplot_E1_cffi_rt <- emm_E1_rt_fi[1:4] %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(. ~ Congruency, switch = "both") +
coord_cartesian(ylim = ylimit_cf_fi_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(RT~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E1_fi_rt.pdf", plot_E1_cffi_rt, width = 7, height = 4.55)
plot_E1_cffi_rt
plot_E1_cf_rt_ <- plot_E1_cf_rt +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.55, 0.075),
legend.box = "horizontal")
plot_E1_rt <- ggarrange(plot_E1_cf_rt_, plot_E1_cffi_rt,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E1_rt.pdf", plot_E1_rt, width = 10, height = 4.5)
plot_E1_rt
2.2.2.4 Comparisons between facilitation and interference
contrast(emm_E1_rt_fi, method = list("faci-inte"=c(1, 1)), by = "Cue")[1:2] %>%
summary(infer = TRUE)## contrast Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top -25.6 20.9 Inf -66.6 15.33 -1.226 0.2201
## faci-inte bottom -48.8 23.3 Inf -94.4 -3.19 -2.097 0.0360
##
## Confidence level used: 0.953 Experiment 2
df_lmm_E2 <- df_lmm %>%
filter(Experiment != "109_cue") %>%
droplevels()
contrasts(df_lmm_E2$Probability) <- MASS::contr.sdif(2)
df_lmm_E2 <- df_lmm_E2 %>%
mutate(Pro_C = if_else(Probability == 0.25, -0.5, 0.5),
Cue_Pro = Cue_C * Pro_C,
Con_Pro = Con_C * Pro_C,
Ali_Pro = Ali_C * Pro_C,
Sam_Pro = Sam_C * Pro_C,
Cue_Con_Pro = Cue_Con * Pro_C,
Cue_Ali_Pro = Cue_Ali * Pro_C,
Cue_Sam_Pro = Cue_Sam * Pro_C,
Con_Ali_Pro = Con_Ali * Pro_C,
Con_Sam_Pro = Con_Sam * Pro_C,
Ali_Sam_Pro = Ali_Sam * Pro_C,
Cue_Con_Ali_Pro = Cue_Con_Ali * Pro_C,
Cue_Con_Sam_Pro = Cue_Con_Sam * Pro_C,
Cue_Ali_Sam_Pro = Cue_Ali_Sam * Pro_C,
Con_Ali_Sam_Pro = Con_Ali_Sam * Pro_C,
Cue_Con_Ali_Sam_Pro = Cue_Con_Ali_Sam * Pro_C
)
# save(df_lmm_E2, file = file.path("data", "df_lmm_E2.RData"))There were 32 participants in Experiment 2.
3.1 Response (d’)
3.1.1 Fitting the generalized mixed models
3.1.1.1 The maximal model
# file_E2_resp_max <- file.path(folder_lmm, "E2_Resp_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_E2_resp_max)) {
# glmm_E2_resp_max <- glmer(
# Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
# (Cue * Congruency * Alignment * SameDifferent * Probability | Participant), # Con_Ali_Sam
# family = binomial(link = "probit"),
# data = df_lmm_E2,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_E2_resp_max, file = file_E2_resp_max)
# } else {
# load(file_E2_resp_max)
# }
#
# print(summary(glmm_E2_resp_max), corr = FALSE)3.1.1.2 The zero-correlation-parameter model
file_E2_resp_zcp <- file.path(folder_lmm, "E2_Resp_lmm_zcp.RData")
# fit the zcp model
if (!file.exists(file_E2_resp_zcp)) {
glmm_E2_resp_zcp <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(Cue_C + Con_C + Ali_C + Sam_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam +
Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam +
Pro_C +
Cue_Pro + Con_Pro + Ali_Pro + Sam_Pro +
Cue_Con_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Ali_Pro + Con_Sam_Pro + Ali_Sam_Pro +
Cue_Con_Ali_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Con_Ali_Sam_Pro +
Cue_Con_Ali_Sam_Pro || Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_zcp, file = file_E2_resp_zcp)
} else {
load(file_E2_resp_zcp)
}
print(summary(glmm_E2_resp_zcp), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam + Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Con_Pro + Ali_Pro + Sam_Pro + Cue_Con_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Ali_Pro + Con_Sam_Pro + Ali_Sam_Pro + Cue_Con_Ali_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Con_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39518.4 40070.1 -19695.2 39390.4 40896
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.0859 -0.5478 0.1864 0.5144 6.1841
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 7.235e-02 2.690e-01
## Participant.1 Cue_C 1.301e-01 3.606e-01
## Participant.2 Con_C 5.310e-03 7.287e-02
## Participant.3 Ali_C 3.194e-02 1.787e-01
## Participant.4 Sam_C 2.027e-01 4.502e-01
## Participant.5 Cue_Con 8.565e-04 2.927e-02
## Participant.6 Cue_Ali 3.749e-02 1.936e-01
## Participant.7 Cue_Sam 5.871e-01 7.662e-01
## Participant.8 Con_Ali 0.000e+00 0.000e+00
## Participant.9 Con_Sam 3.870e-01 6.221e-01
## Participant.10 Ali_Sam 0.000e+00 0.000e+00
## Participant.11 Cue_Con_Ali 0.000e+00 0.000e+00
## Participant.12 Cue_Con_Sam 1.168e+00 1.081e+00
## Participant.13 Cue_Ali_Sam 3.098e-09 5.566e-05
## Participant.14 Con_Ali_Sam 1.058e-01 3.253e-01
## Participant.15 Cue_Con_Ali_Sam 7.473e-02 2.734e-01
## Participant.16 Pro_C 5.746e-02 2.397e-01
## Participant.17 Cue_Pro 4.125e-01 6.422e-01
## Participant.18 Con_Pro 1.446e-03 3.803e-02
## Participant.19 Ali_Pro 2.664e-03 5.161e-02
## Participant.20 Sam_Pro 4.237e-02 2.058e-01
## Participant.21 Cue_Con_Pro 1.238e-10 1.113e-05
## Participant.22 Cue_Ali_Pro 5.495e-02 2.344e-01
## Participant.23 Cue_Sam_Pro 1.568e+00 1.252e+00
## Participant.24 Con_Ali_Pro 4.282e-08 2.069e-04
## Participant.25 Con_Sam_Pro 1.252e-01 3.538e-01
## Participant.26 Ali_Sam_Pro 0.000e+00 0.000e+00
## Participant.27 Cue_Con_Ali_Pro 1.121e-10 1.059e-05
## Participant.28 Cue_Con_Sam_Pro 2.502e+00 1.582e+00
## Participant.29 Cue_Ali_Sam_Pro 7.879e-02 2.807e-01
## Participant.30 Con_Ali_Sam_Pro 0.000e+00 0.000e+00
## Participant.31 Cue_Con_Ali_Sam_Pro 7.265e-02 2.695e-01
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.167240 0.096271 12.125 < 2e-16 ***
## Cuebottom 0.136779 0.120487 1.135 0.256284
## Congruencyincongruent -0.924275 0.090843 -10.174 < 2e-16 ***
## Alignmentmisaligned -0.162074 0.064753 -2.503 0.012316 *
## SameDifferentdifferent -2.085094 0.139008 -15.000 < 2e-16 ***
## Probability2-1 0.504956 0.127782 3.952 7.76e-05 ***
## Cuebottom:Congruencyincongruent 0.078762 0.120912 0.651 0.514790
## Cuebottom:Alignmentmisaligned -0.004857 0.082901 -0.059 0.953278
## Congruencyincongruent:Alignmentmisaligned 0.528911 0.075136 7.039 1.93e-12 ***
## Cuebottom:SameDifferentdifferent 0.141044 0.183222 0.770 0.441419
## Congruencyincongruent:SameDifferentdifferent 1.488729 0.164982 9.024 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.310225 0.076795 4.040 5.35e-05 ***
## Cuebottom:Probability2-1 -0.809106 0.211692 -3.822 0.000132 ***
## Congruencyincongruent:Probability2-1 0.111238 0.126787 0.877 0.380289
## Alignmentmisaligned:Probability2-1 -0.063634 0.107096 -0.594 0.552396
## SameDifferentdifferent:Probability2-1 -0.791074 0.177872 -4.447 8.69e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.318486 0.100998 -3.153 0.001614 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.221842 0.217551 -1.020 0.307860
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.122133 0.102062 -1.197 0.231440
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.813040 0.112991 -7.196 6.22e-13 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.429262 0.203762 -2.107 0.035145 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.040635 0.158902 0.256 0.798162
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.118865 0.138386 0.859 0.390376
## Cuebottom:SameDifferentdifferent:Probability2-1 1.359361 0.309491 4.392 1.12e-05 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.262296 0.208444 -1.258 0.208266
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.171116 0.144253 1.186 0.235533
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.600009 0.141603 4.237 2.26e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.146778 0.199783 -0.735 0.462528
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.778487 0.347609 2.240 0.025120 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.135719 0.209018 -0.649 0.516132
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.291421 0.192026 -1.518 0.129112
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.441127 0.274619 1.606 0.108203
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingular3.1.1.3 The reduced model
summary(rePCA(glmm_E2_resp_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32]
## Standard deviation 1.582 1.2521 1.0807 0.76621 0.64223 0.62211 0.45022 0.36064 0.35380 0.3253 0.2807 0.27336 0.26953 0.26898 0.23971 0.23442 0.20585 0.19362 0.17872 0.07287 0.05161 0.03803 0.02927 0.0002069 5.566e-05 1.113e-05 1.059e-05 1.58e-16 1.58e-16 1.58e-16 1.58e-16 1.58e-16
## Proportion of Variance 0.324 0.2031 0.1513 0.07604 0.05342 0.05013 0.02625 0.01685 0.01621 0.0137 0.0102 0.00968 0.00941 0.00937 0.00744 0.00712 0.00549 0.00486 0.00414 0.00069 0.00035 0.00019 0.00011 0.0000000 0.000e+00 0.000e+00 0.000e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
## Cumulative Proportion 0.324 0.5271 0.6784 0.75440 0.80782 0.85795 0.88420 0.90105 0.91726 0.9310 0.9412 0.95085 0.96026 0.96963 0.97707 0.98419 0.98968 0.99453 0.99867 0.99936 0.99970 0.99989 1.00000 1.0000000 1.000e+00 1.000e+00 1.000e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00Con_Ali, Ali_Sam, Cue_Con_Ali, Ali_Sam_Pro, Con_Ali_Sam_Pro, Cue_Con_Pro, Cue_Con_Ali_Pro, Cue_Ali_Sam, Con_Ali_Pro, Cue_Con, Con_C, Con_Pro, and Ali_Pro were removed from extended model (glmm_E2_resp_zcp) due to that the variances they explained were smaller than 0.1%, making glmm_E2_resp_rdc.
file_E2_resp_rdc <- file.path(folder_lmm, "E2_Resp_lmm_rdc.RData")
# fit the rdc model
if (!file.exists(file_E2_resp_rdc)) {
glmm_E2_resp_rdc <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(Cue_C + Ali_C + Sam_C + # Con_C +
Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con +
Cue_Con_Sam + Con_Ali_Sam + # Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam +
Pro_C +
Cue_Pro + Sam_Pro + # Con_Pro + Ali_Pro +
Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro +
Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro +
Cue_Con_Ali_Sam_Pro || Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_rdc, file = file_E2_resp_rdc)
} else {
load(file_E2_resp_rdc)
}
print(summary(glmm_E2_resp_rdc), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Ali_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39499.3 39938.9 -19698.6 39397.3 40909
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.0280 -0.5442 0.1864 0.5132 6.4343
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.07191 0.2682
## Participant.1 Cue_C 0.12974 0.3602
## Participant.2 Ali_C 0.03200 0.1789
## Participant.3 Sam_C 0.20136 0.4487
## Participant.4 Cue_Ali 0.03777 0.1943
## Participant.5 Cue_Sam 0.58652 0.7658
## Participant.6 Con_Sam 0.38686 0.6220
## Participant.7 Cue_Con_Sam 1.16357 1.0787
## Participant.8 Con_Ali_Sam 0.10664 0.3266
## Participant.9 Cue_Con_Ali_Sam 0.07529 0.2744
## Participant.10 Pro_C 0.05742 0.2396
## Participant.11 Cue_Pro 0.41100 0.6411
## Participant.12 Sam_Pro 0.04238 0.2059
## Participant.13 Cue_Ali_Pro 0.05527 0.2351
## Participant.14 Cue_Sam_Pro 1.56194 1.2498
## Participant.15 Con_Sam_Pro 0.12776 0.3574
## Participant.16 Cue_Con_Sam_Pro 2.51204 1.5849
## Participant.17 Cue_Ali_Sam_Pro 0.07806 0.2794
## Participant.18 Cue_Con_Ali_Sam_Pro 0.08202 0.2864
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.161577 0.095404 12.175 < 2e-16 ***
## Cuebottom 0.133927 0.119341 1.122 0.26177
## Congruencyincongruent -0.918154 0.089221 -10.291 < 2e-16 ***
## Alignmentmisaligned -0.161014 0.064543 -2.495 0.01261 *
## SameDifferentdifferent -2.080834 0.138032 -15.075 < 2e-16 ***
## Probability2-1 0.500358 0.124609 4.015 5.93e-05 ***
## Cuebottom:Congruencyincongruent 0.082352 0.119444 0.689 0.49053
## Cuebottom:Alignmentmisaligned -0.003579 0.082497 -0.043 0.96540
## Congruencyincongruent:Alignmentmisaligned 0.528746 0.074825 7.066 1.59e-12 ***
## Cuebottom:SameDifferentdifferent 0.144919 0.181197 0.800 0.42384
## Congruencyincongruent:SameDifferentdifferent 1.484702 0.163887 9.059 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.309695 0.076405 4.053 5.05e-05 ***
## Cuebottom:Probability2-1 -0.799695 0.205177 -3.898 9.72e-05 ***
## Congruencyincongruent:Probability2-1 0.115795 0.124101 0.933 0.35079
## Alignmentmisaligned:Probability2-1 -0.062760 0.104884 -0.598 0.54959
## SameDifferentdifferent:Probability2-1 -0.782907 0.172408 -4.541 5.60e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.320274 0.100435 -3.189 0.00143 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.227217 0.215256 -1.056 0.29117
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.123808 0.101420 -1.221 0.22218
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.813777 0.112578 -7.229 4.88e-13 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.441175 0.198630 -2.221 0.02635 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.039556 0.155778 0.254 0.79955
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.118771 0.136061 0.873 0.38270
## Cuebottom:SameDifferentdifferent:Probability2-1 1.347036 0.298311 4.516 6.32e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.270481 0.204823 -1.321 0.18665
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.169703 0.141541 1.199 0.23054
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.602570 0.140816 4.279 1.88e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.146111 0.196348 -0.744 0.45679
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.792652 0.339792 2.333 0.01966 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.135063 0.204362 -0.661 0.50867
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.291600 0.188664 -1.546 0.12220
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.441772 0.269640 1.638 0.10134
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.0036263 (tol = 0.001, component 1)file_E2_resp_rdc1 <- file.path(folder_lmm, "E2_Resp_lmm_rdc1.RData")
# fit the rdc1 model
if (!file.exists(file_E2_resp_rdc1)) {
ss <- getME(glmm_E2_resp_rdc, c("theta","fixef"))
glmm_E2_resp_rdc1 <- update(
glmm_E2_resp_rdc, start=ss,
control=glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
# save(glmm_E2_resp_rdc1, file = file_E2_resp_rdc1)
} else {
load(file_E2_resp_rdc1)
}
print(summary(glmm_E2_resp_rdc1), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Ali_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39499.3 39938.9 -19698.6 39397.3 40909
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.0280 -0.5442 0.1864 0.5132 6.4344
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.07191 0.2682
## Participant.1 Cue_C 0.12974 0.3602
## Participant.2 Ali_C 0.03200 0.1789
## Participant.3 Sam_C 0.20136 0.4487
## Participant.4 Cue_Ali 0.03777 0.1943
## Participant.5 Cue_Sam 0.58652 0.7658
## Participant.6 Con_Sam 0.38689 0.6220
## Participant.7 Cue_Con_Sam 1.16352 1.0787
## Participant.8 Con_Ali_Sam 0.10663 0.3265
## Participant.9 Cue_Con_Ali_Sam 0.07532 0.2744
## Participant.10 Pro_C 0.05742 0.2396
## Participant.11 Cue_Pro 0.41100 0.6411
## Participant.12 Sam_Pro 0.04238 0.2059
## Participant.13 Cue_Ali_Pro 0.05528 0.2351
## Participant.14 Cue_Sam_Pro 1.56195 1.2498
## Participant.15 Con_Sam_Pro 0.12775 0.3574
## Participant.16 Cue_Con_Sam_Pro 2.51212 1.5850
## Participant.17 Cue_Ali_Sam_Pro 0.07809 0.2795
## Participant.18 Cue_Con_Ali_Sam_Pro 0.08224 0.2868
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.161644 0.095789 12.127 < 2e-16 ***
## Cuebottom 0.133884 0.119940 1.116 0.264310
## Congruencyincongruent -0.918241 0.089631 -10.245 < 2e-16 ***
## Alignmentmisaligned -0.161054 0.064846 -2.484 0.013005 *
## SameDifferentdifferent -2.080951 0.138735 -14.999 < 2e-16 ***
## Probability2-1 0.500269 0.126476 3.955 7.64e-05 ***
## Cuebottom:Congruencyincongruent 0.082398 0.120225 0.685 0.493116
## Cuebottom:Alignmentmisaligned -0.003555 0.082858 -0.043 0.965777
## Congruencyincongruent:Alignmentmisaligned 0.528811 0.075317 7.021 2.20e-12 ***
## Cuebottom:SameDifferentdifferent 0.145001 0.182228 0.796 0.426201
## Congruencyincongruent:SameDifferentdifferent 1.484846 0.164570 9.023 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.309744 0.076963 4.025 5.71e-05 ***
## Cuebottom:Probability2-1 -0.799515 0.208879 -3.828 0.000129 ***
## Congruencyincongruent:Probability2-1 0.115955 0.125358 0.925 0.354972
## Alignmentmisaligned:Probability2-1 -0.062710 0.106376 -0.590 0.555521
## SameDifferentdifferent:Probability2-1 -0.782734 0.175982 -4.448 8.68e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.320322 0.101029 -3.171 0.001521 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.227313 0.216593 -1.049 0.293950
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.123835 0.102075 -1.213 0.225065
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.813867 0.113356 -7.180 6.98e-13 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.441463 0.201487 -2.191 0.028450 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.039470 0.158284 0.249 0.803082
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.118690 0.138420 0.857 0.391191
## Cuebottom:SameDifferentdifferent:Probability2-1 1.346692 0.304851 4.418 9.98e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.270748 0.207217 -1.307 0.191353
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.169636 0.144319 1.175 0.239825
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.602634 0.141749 4.251 2.12e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.145973 0.200610 -0.728 0.466829
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.793152 0.344651 2.301 0.021374 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.134931 0.208670 -0.647 0.517875
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.291497 0.193049 -1.510 0.131053
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.441598 0.276719 1.596 0.110525
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00152842 (tol = 0.001, component 1)Ali_C was further removed.
file_E2_resp_rdc2 <- file.path(folder_lmm, "E2_Resp_lmm_rdc2.RData")
# fit the rdc2 model
if (!file.exists(file_E2_resp_rdc2)) {
glmm_E2_resp_rdc2 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con +
Cue_Con_Sam + Con_Ali_Sam + # Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam +
Pro_C +
Cue_Pro + Sam_Pro + # Con_Pro + Ali_Pro +
Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro +
Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro +
Cue_Con_Ali_Sam_Pro || Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_rdc2, file = file_E2_resp_rdc2)
} else {
load(file_E2_resp_rdc2)
}
print(summary(glmm_E2_resp_rdc2), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39575.2 40006.3 -19737.6 39475.2 40910
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.6455 -0.5528 0.1967 0.5113 5.7139
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.07145 0.2673
## Participant.1 Cue_C 0.12947 0.3598
## Participant.2 Sam_C 0.19931 0.4464
## Participant.3 Cue_Ali 0.04192 0.2047
## Participant.4 Cue_Sam 0.58683 0.7660
## Participant.5 Con_Sam 0.38364 0.6194
## Participant.6 Cue_Con_Sam 1.15766 1.0759
## Participant.7 Con_Ali_Sam 0.10035 0.3168
## Participant.8 Cue_Con_Ali_Sam 0.07774 0.2788
## Participant.9 Pro_C 0.05713 0.2390
## Participant.10 Cue_Pro 0.40833 0.6390
## Participant.11 Sam_Pro 0.04196 0.2048
## Participant.12 Cue_Ali_Pro 0.10085 0.3176
## Participant.13 Cue_Sam_Pro 1.54889 1.2445
## Participant.14 Con_Sam_Pro 0.12625 0.3553
## Participant.15 Cue_Con_Sam_Pro 2.48434 1.5762
## Participant.16 Cue_Ali_Sam_Pro 0.08956 0.2993
## Participant.17 Cue_Con_Ali_Sam_Pro 0.09184 0.3030
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.164756 0.093859 12.410 < 2e-16 ***
## Cuebottom 0.133595 0.119396 1.119 0.26317
## Congruencyincongruent -0.919451 0.088659 -10.371 < 2e-16 ***
## Alignmentmisaligned -0.175552 0.056182 -3.125 0.00178 **
## SameDifferentdifferent -2.082488 0.137486 -15.147 < 2e-16 ***
## Probability2-1 0.504191 0.124335 4.055 5.01e-05 ***
## Cuebottom:Congruencyincongruent 0.082452 0.119261 0.691 0.48934
## Cuebottom:Alignmentmisaligned -0.002788 0.083158 -0.034 0.97325
## Congruencyincongruent:Alignmentmisaligned 0.535632 0.074313 7.208 5.69e-13 ***
## Cuebottom:SameDifferentdifferent 0.144981 0.180905 0.801 0.42289
## Congruencyincongruent:SameDifferentdifferent 1.484362 0.162668 9.125 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.327358 0.075751 4.322 1.55e-05 ***
## Cuebottom:Probability2-1 -0.800391 0.204913 -3.906 9.38e-05 ***
## Congruencyincongruent:Probability2-1 0.113429 0.123145 0.921 0.35699
## Alignmentmisaligned:Probability2-1 -0.071931 0.106629 -0.675 0.49994
## SameDifferentdifferent:Probability2-1 -0.786107 0.171382 -4.587 4.50e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.319841 0.100426 -3.185 0.00145 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.226218 0.214466 -1.055 0.29152
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.126699 0.101285 -1.251 0.21097
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.820362 0.111485 -7.358 1.86e-13 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.441981 0.197312 -2.240 0.02509 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.041045 0.160452 0.256 0.79810
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.120043 0.136301 0.881 0.37847
## Cuebottom:SameDifferentdifferent:Probability2-1 1.351061 0.297076 4.548 5.42e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.270287 0.202271 -1.336 0.18146
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.179901 0.141997 1.267 0.20518
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.601164 0.140948 4.265 2.00e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.134248 0.196907 -0.682 0.49538
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.790854 0.336433 2.351 0.01874 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.144169 0.205911 -0.700 0.48383
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.284773 0.188893 -1.508 0.13166
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.426096 0.270915 1.573 0.11576
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.1.1.4 The extended model
file_E2_resp_etd <- file.path(folder_lmm, "E2_Resp_lmm_etd.RData")
# fit the etd model
if (!file.exists(file_E2_resp_etd)) {
glmm_E2_resp_etd <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con +
Cue_Con_Sam + Con_Ali_Sam + # Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam +
Pro_C +
Cue_Pro + Sam_Pro + # Con_Pro + Ali_Pro +
Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro +
Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro +
Cue_Con_Ali_Sam_Pro | Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_etd, file = file_E2_resp_etd)
} else {
load(file_E2_resp_etd)
}
print(summary(glmm_E2_resp_etd), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39642.9 41392.8 -19618.4 39236.9 40757
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.1243 -0.5461 0.1847 0.5087 5.4164
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.07234 0.2690
## Cue_C 0.13027 0.3609 -0.24
## Sam_C 0.19650 0.4433 -0.28 -0.08
## Cue_Ali 0.04713 0.2171 -0.45 -0.06 0.48
## Cue_Sam 0.56720 0.7531 0.02 -0.05 0.11 -0.15
## Con_Sam 0.41210 0.6420 -0.02 -0.12 -0.12 -0.13 0.24
## Cue_Con_Sam 1.24842 1.1173 -0.07 -0.12 0.12 -0.11 0.93 0.34
## Con_Ali_Sam 0.12819 0.3580 0.03 0.24 0.36 0.22 0.40 -0.48 0.36
## Cue_Con_Ali_Sam 0.14618 0.3823 -0.20 -0.05 -0.38 0.11 -0.43 -0.04 -0.35 -0.33
## Pro_C 0.05618 0.2370 0.08 -0.06 -0.41 -0.25 0.01 0.56 0.15 -0.23 -0.06
## Cue_Pro 0.41443 0.6438 0.25 -0.35 -0.05 0.16 0.00 -0.01 -0.04 0.04 -0.29 0.17
## Sam_Pro 0.04925 0.2219 -0.10 0.66 -0.20 0.09 -0.17 -0.11 -0.19 0.11 -0.31 0.04 0.18
## Cue_Ali_Pro 0.10190 0.3192 -0.05 0.01 -0.04 -0.13 0.26 0.10 0.32 0.25 -0.16 0.08 -0.14 -0.04
## Cue_Sam_Pro 1.50213 1.2256 -0.10 0.37 -0.40 0.17 -0.22 -0.19 -0.13 -0.04 0.48 0.00 -0.07 0.24 -0.11
## Con_Sam_Pro 0.16649 0.4080 -0.37 0.28 0.11 0.42 0.20 0.01 0.29 0.41 0.36 -0.32 -0.45 0.01 0.30 0.34
## Cue_Con_Sam_Pro 2.68063 1.6373 -0.23 0.25 0.10 0.17 -0.07 0.55 -0.01 -0.26 0.25 0.04 -0.25 0.01 0.04 0.28 0.44
## Cue_Ali_Sam_Pro 0.30480 0.5521 -0.10 -0.02 0.10 -0.14 0.20 0.12 0.10 -0.08 0.10 0.18 -0.08 -0.57 -0.18 0.10 -0.18 0.19
## Cue_Con_Ali_Sam_Pro 1.29026 1.1359 0.39 -0.14 -0.27 -0.16 -0.02 -0.68 -0.14 0.27 -0.12 -0.37 0.48 0.19 0.05 0.05 -0.27 -0.70 -0.34
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.16378 0.09577 12.152 < 2e-16 ***
## Cuebottom 0.13693 0.08922 1.535 0.12482
## Congruencyincongruent -0.92047 0.09260 -9.940 < 2e-16 ***
## Alignmentmisaligned -0.17366 0.05836 -2.976 0.00292 **
## SameDifferentdifferent -2.08752 0.12560 -16.620 < 2e-16 ***
## Probability2-1 0.50859 0.11888 4.278 1.89e-05 ***
## Cuebottom:Congruencyincongruent 0.08571 0.12854 0.667 0.50489
## Cuebottom:Alignmentmisaligned -0.02252 0.08692 -0.259 0.79560
## Congruencyincongruent:Alignmentmisaligned 0.53997 0.08036 6.720 1.82e-11 ***
## Cuebottom:SameDifferentdifferent 0.14393 0.08868 1.623 0.10458
## Congruencyincongruent:SameDifferentdifferent 1.49226 0.17075 8.739 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.33908 0.08183 4.144 3.42e-05 ***
## Cuebottom:Probability2-1 -0.81784 0.20095 -4.070 4.70e-05 ***
## Congruencyincongruent:Probability2-1 0.10829 0.13738 0.788 0.43054
## Alignmentmisaligned:Probability2-1 -0.08277 0.12098 -0.684 0.49385
## SameDifferentdifferent:Probability2-1 -0.76710 0.17398 -4.409 1.04e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.31111 0.10459 -2.975 0.00293 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.23602 0.23437 -1.007 0.31393
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.11179 0.10543 -1.060 0.28900
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.84234 0.12582 -6.695 2.16e-11 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.43512 0.24535 -1.773 0.07615 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.05710 0.19223 0.297 0.76644
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.14020 0.15284 0.917 0.35897
## Cuebottom:SameDifferentdifferent:Probability2-1 1.33822 0.31295 4.276 1.90e-05 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.28488 0.23036 -1.237 0.21621
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.16430 0.17149 0.958 0.33804
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.60574 0.15049 4.025 5.70e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.15098 0.23349 -0.647 0.51788
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.81564 0.43657 1.868 0.06172 .
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.12617 0.27134 -0.465 0.64192
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.27745 0.22776 -1.218 0.22316
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.40220 0.35575 1.131 0.25825
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E2_resp_etd))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18]
## Standard deviation 1.9646 1.4686 1.1837 0.76286 0.68384 0.57853 0.48431 0.41992 0.30652 0.28379 0.24972 0.1799 0.14908 0.10023 0.01389 0.003311 0.0003458 7.185e-21
## Proportion of Variance 0.4057 0.2267 0.1473 0.06117 0.04915 0.03518 0.02465 0.01853 0.00987 0.00846 0.00655 0.0034 0.00234 0.00106 0.00002 0.000000 0.0000000 0.000e+00
## Cumulative Proportion 0.4057 0.6323 0.7796 0.84078 0.88993 0.92510 0.94976 0.96829 0.97816 0.98663 0.99318 0.9966 0.99892 0.99998 1.00000 1.000000 1.0000000 1.000e+00Sam_Pro, Cue_Ali, Pro_C, Intercept, Cue_Ali_Pro, Con_Ali_Sam, Cue_C, Cue_Con_Ali_Sam, Con_Sam_Pro, and Sam_C were removed from extended model (glmm_E2_resp_etd) due to that the variances they explained were smaller than 1%, making glmm_E2_resp_etd1.
file_E2_resp_etd1 <- file.path(folder_lmm, "E2_Resp_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_E2_resp_etd1)) {
glmm_E2_resp_etd1 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
# Cue_Con_Ali_Sam +
# Pro_C +
Cue_Pro + # Con_Pro + Ali_Pro + Sam_Pro +
Cue_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro + Cue_Ali_Pro + Con_Sam_Pro +
Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro +
Cue_Con_Ali_Sam_Pro | Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_etd1, file = file_E2_resp_etd1)
} else {
load(file_E2_resp_etd1)
}
print(summary(glmm_E2_resp_etd1), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Pro + Cue_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 41926.0 42512.2 -20895.0 41790.0 40892
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3720 -0.5860 0.2749 0.5384 3.5224
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5906 0.7685
## Con_Sam 0.3907 0.6251 0.22
## Cue_Con_Sam 1.0738 1.0363 0.87 0.37
## Cue_Pro 0.4212 0.6490 -0.07 0.03 0.04
## Cue_Sam_Pro 2.5569 1.5990 -0.24 -0.09 -0.18 0.01
## Cue_Con_Sam_Pro 2.2046 1.4848 -0.01 0.57 -0.08 -0.10 0.19
## Cue_Ali_Sam_Pro 0.1210 0.3478 0.32 0.17 0.03 -0.05 0.16 0.40
## Cue_Con_Ali_Sam_Pro 0.6926 0.8322 -0.39 -0.56 -0.31 0.26 0.28 -0.72 -0.58
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.065368 0.047269 22.538 < 2e-16 ***
## Cuebottom 0.126927 0.062066 2.045 0.040851 *
## Congruencyincongruent -0.822358 0.073228 -11.230 < 2e-16 ***
## Alignmentmisaligned -0.162130 0.047841 -3.389 0.000702 ***
## SameDifferentdifferent -1.918752 0.079915 -24.010 < 2e-16 ***
## Probability2-1 0.463426 0.116323 3.984 6.78e-05 ***
## Cuebottom:Congruencyincongruent 0.057438 0.112941 0.509 0.611054
## Cuebottom:Alignmentmisaligned 0.006756 0.069246 0.098 0.922276
## Congruencyincongruent:Alignmentmisaligned 0.484561 0.064370 7.528 5.16e-14 ***
## Cuebottom:SameDifferentdifferent 0.123210 0.098882 1.246 0.212753
## Congruencyincongruent:SameDifferentdifferent 1.346494 0.130855 10.290 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.304934 0.065923 4.626 3.74e-06 ***
## Cuebottom:Probability2-1 -0.751581 0.212449 -3.538 0.000404 ***
## Congruencyincongruent:Probability2-1 0.105583 0.121221 0.871 0.383757
## Alignmentmisaligned:Probability2-1 -0.070257 0.100458 -0.699 0.484326
## SameDifferentdifferent:Probability2-1 -0.761049 0.184328 -4.129 3.65e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.288252 0.092384 -3.120 0.001808 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.178150 0.204170 -0.873 0.382906
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.131320 0.093467 -1.405 0.160024
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.754975 0.089568 -8.429 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.400302 0.206614 -1.937 0.052692 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.030144 0.151694 0.199 0.842484
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.107291 0.134283 0.799 0.424297
## Cuebottom:SameDifferentdifferent:Probability2-1 1.303589 0.343517 3.795 0.000148 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.239896 0.203854 -1.177 0.239274
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.177388 0.145468 1.219 0.222681
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.556425 0.126888 4.385 1.16e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.120176 0.199616 -0.602 0.547151
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.727077 0.365982 1.987 0.046962 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.134409 0.224072 -0.600 0.548606
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.259861 0.194882 -1.333 0.182392
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.401627 0.296117 1.356 0.175000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E2_resp_etd1))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## Standard deviation 1.735 1.6457 1.1942 0.6756 0.49154 0.36189 0.27765 1.039e-05
## Proportion of Variance 0.374 0.3364 0.1771 0.0567 0.03001 0.01627 0.00957 0.000e+00
## Cumulative Proportion 0.374 0.7103 0.8874 0.9442 0.97416 0.99043 1.00000 1.000e+00Cue_Ali_Sam_Pro, and Con_Sam were removed from extended model (glmm_E2_resp_etd1) due to that the variances they explained were smaller than 1%, making glmm_E2_resp_etd2.
file_E2_resp_etd2 <- file.path(folder_lmm, "E2_Resp_lmm_etd2.RData")
# fit the etd2 model
if (!file.exists(file_E2_resp_etd2)) {
glmm_E2_resp_etd2 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali + Con_Sam +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
# Cue_Con_Ali_Sam +
# Pro_C +
Cue_Pro + # Con_Pro + Ali_Pro + Sam_Pro +
Cue_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro + Cue_Ali_Pro + Con_Sam_Pro +
Cue_Con_Sam_Pro + # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro + Cue_Ali_Sam_Pro +
Cue_Con_Ali_Sam_Pro | Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_etd2, file = file_E2_resp_etd2)
} else {
load(file_E2_resp_etd2)
}
print(summary(glmm_E2_resp_etd2), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Cue_Con_Sam + Cue_Pro + Cue_Sam_Pro + Cue_Con_Sam_Pro + Cue_Con_Ali_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 42204.6 42661.5 -21049.3 42098.6 40907
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.7184 -0.6074 0.2827 0.5353 4.0992
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5933 0.7702
## Cue_Con_Sam 1.1571 1.0757 0.87
## Cue_Pro 0.4151 0.6443 -0.08 0.03
## Cue_Sam_Pro 2.5745 1.6045 -0.25 -0.18 0.01
## Cue_Con_Sam_Pro 1.7821 1.3349 -0.20 -0.41 -0.10 0.27
## Cue_Con_Ali_Sam_Pro 0.3644 0.6037 -0.49 -0.45 0.40 0.42 -0.38
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.05243 0.03888 27.070 < 2e-16 ***
## Cuebottom 0.11590 0.06142 1.887 0.059138 .
## Congruencyincongruent -0.80308 0.06609 -12.151 < 2e-16 ***
## Alignmentmisaligned -0.15843 0.04741 -3.341 0.000833 ***
## SameDifferentdifferent -1.89558 0.05949 -31.862 < 2e-16 ***
## Probability2-1 0.48478 0.11363 4.266 1.99e-05 ***
## Cuebottom:Congruencyincongruent 0.06424 0.11584 0.555 0.579230
## Cuebottom:Alignmentmisaligned 0.01383 0.06842 0.202 0.839856
## Congruencyincongruent:Alignmentmisaligned 0.48017 0.06396 7.508 6.02e-14 ***
## Cuebottom:SameDifferentdifferent 0.13255 0.09821 1.350 0.177113
## Congruencyincongruent:SameDifferentdifferent 1.30716 0.11474 11.392 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.30055 0.06536 4.599 4.25e-06 ***
## Cuebottom:Probability2-1 -0.81512 0.20646 -3.948 7.88e-05 ***
## Congruencyincongruent:Probability2-1 0.07572 0.11354 0.667 0.504852
## Alignmentmisaligned:Probability2-1 -0.08504 0.09628 -0.883 0.377094
## SameDifferentdifferent:Probability2-1 -0.80384 0.17693 -4.543 5.54e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.29510 0.09145 -3.227 0.001251 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.17733 0.21100 -0.840 0.400663
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13908 0.09256 -1.503 0.132953
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.74693 0.08906 -8.387 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.31900 0.18803 -1.697 0.089788 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.06144 0.14100 0.436 0.663031
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.12029 0.13133 0.916 0.359701
## Cuebottom:SameDifferentdifferent:Probability2-1 1.39844 0.32765 4.268 1.97e-05 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.17425 0.18472 -0.943 0.345528
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.20587 0.13419 1.534 0.124989
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.55866 0.12589 4.438 9.09e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.14669 0.19247 -0.762 0.445969
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.59352 0.32247 1.841 0.065690 .
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.18205 0.19499 -0.934 0.350503
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.28687 0.18706 -1.534 0.125135
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.44075 0.27631 1.595 0.110683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.00161086 (tol = 0.001, component 1)file_E2_resp_etd3 <- file.path(folder_lmm, "E2_Resp_lmm_etd3.RData")
# fit the etd3 model
if (!file.exists(file_E2_resp_etd3)) {
ss <- getME(glmm_E2_resp_etd2, c("theta","fixef"))
glmm_E2_resp_etd3 <- update(
glmm_E2_resp_etd2, start=ss,
control=glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
# save(glmm_E2_resp_etd3, file = file_E2_resp_etd3)
} else {
load(file_E2_resp_etd3)
}
print(summary(glmm_E2_resp_etd3), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Cue_Con_Sam + Cue_Pro + Cue_Sam_Pro + Cue_Con_Sam_Pro + Cue_Con_Ali_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 42204.6 42661.5 -21049.3 42098.6 40907
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.7184 -0.6074 0.2827 0.5353 4.0992
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5932 0.7702
## Cue_Con_Sam 1.1569 1.0756 0.87
## Cue_Pro 0.4151 0.6443 -0.08 0.03
## Cue_Sam_Pro 2.5747 1.6046 -0.25 -0.18 0.01
## Cue_Con_Sam_Pro 1.7820 1.3349 -0.20 -0.41 -0.10 0.27
## Cue_Con_Ali_Sam_Pro 0.3644 0.6036 -0.49 -0.45 0.40 0.42 -0.38
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.05243 0.03867 27.213 < 2e-16 ***
## Cuebottom 0.11590 0.06120 1.894 0.058249 .
## Congruencyincongruent -0.80308 0.06549 -12.263 < 2e-16 ***
## Alignmentmisaligned -0.15843 0.04723 -3.354 0.000795 ***
## SameDifferentdifferent -1.89558 0.05906 -32.098 < 2e-16 ***
## Probability2-1 0.48478 0.11188 4.333 1.47e-05 ***
## Cuebottom:Congruencyincongruent 0.06424 0.11484 0.559 0.575917
## Cuebottom:Alignmentmisaligned 0.01383 0.06823 0.203 0.839430
## Congruencyincongruent:Alignmentmisaligned 0.48017 0.06363 7.546 4.47e-14 ***
## Cuebottom:SameDifferentdifferent 0.13255 0.09775 1.356 0.175109
## Congruencyincongruent:SameDifferentdifferent 1.30716 0.11366 11.501 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.30055 0.06492 4.630 3.66e-06 ***
## Cuebottom:Probability2-1 -0.81512 0.20305 -4.014 5.96e-05 ***
## Congruencyincongruent:Probability2-1 0.07572 0.11037 0.686 0.492703
## Alignmentmisaligned:Probability2-1 -0.08504 0.09467 -0.898 0.368998
## SameDifferentdifferent:Probability2-1 -0.80384 0.17290 -4.649 3.34e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.29510 0.09113 -3.238 0.001202 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.17733 0.20925 -0.847 0.396728
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13908 0.09211 -1.510 0.131055
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.74693 0.08833 -8.457 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.31900 0.18157 -1.757 0.078940 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.06144 0.13778 0.446 0.655674
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.12029 0.12891 0.933 0.350730
## Cuebottom:SameDifferentdifferent:Probability2-1 1.39844 0.32002 4.370 1.24e-05 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.17425 0.17857 -0.976 0.329167
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.20587 0.13109 1.570 0.116314
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.55866 0.12517 4.463 8.07e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.14669 0.18728 -0.783 0.433455
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.59352 0.31060 1.911 0.056024 .
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.18205 0.18920 -0.962 0.335966
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.28687 0.18205 -1.576 0.115074
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.44075 0.26661 1.653 0.098299 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.0021675 (tol = 0.001, component 1)summary(rePCA(glmm_E2_resp_etd3))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6]
## Standard deviation 1.7897 1.3385 1.1614 0.65483 0.33749 0.0001623
## Proportion of Variance 0.4652 0.2602 0.1959 0.06227 0.01654 0.0000000
## Cumulative Proportion 0.4652 0.7253 0.9212 0.98346 1.00000 1.0000000Cue_Con_Ali_Sam_Pro was removed from extended model (glmm_E2_resp_etd3) due to that the variances it explained were smaller than 1%, making glmm_E2_resp_etd4.
file_E2_resp_etd4 <- file.path(folder_lmm, "E2_Resp_lmm_etd4.RData")
# fit the etd4 model
if (!file.exists(file_E2_resp_etd4)) {
glmm_E2_resp_etd4 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali + Con_Sam +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
# Cue_Con_Ali_Sam +
# Pro_C +
Cue_Pro + # Con_Pro + Ali_Pro + Sam_Pro +
Cue_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro + Cue_Ali_Pro + Con_Sam_Pro +
Cue_Con_Sam_Pro # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro + Cue_Ali_Sam_Pro + + Cue_Con_Ali_Sam_Pro
| Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_etd4, file = file_E2_resp_etd4)
} else {
load(file_E2_resp_etd4)
}
print(summary(glmm_E2_resp_etd4), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Cue_Con_Sam + Cue_Pro + Cue_Sam_Pro + Cue_Con_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 42198.4 42603.6 -21052.2 42104.4 40913
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.4599 -0.6086 0.2839 0.5376 4.0136
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5939 0.7707
## Cue_Con_Sam 1.1556 1.0750 0.87
## Cue_Pro 0.4156 0.6447 -0.08 0.03
## Cue_Sam_Pro 2.5692 1.6029 -0.24 -0.18 0.01
## Cue_Con_Sam_Pro 1.7694 1.3302 -0.20 -0.41 -0.10 0.27
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.05176 0.03874 27.147 < 2e-16 ***
## Cuebottom 0.11557 0.06129 1.886 0.059347 .
## Congruencyincongruent -0.80278 0.06584 -12.194 < 2e-16 ***
## Alignmentmisaligned -0.15744 0.04727 -3.331 0.000866 ***
## SameDifferentdifferent -1.89315 0.05924 -31.959 < 2e-16 ***
## Probability2-1 0.48388 0.11091 4.363 1.29e-05 ***
## Cuebottom:Congruencyincongruent 0.06502 0.11547 0.563 0.573373
## Cuebottom:Alignmentmisaligned 0.01428 0.06836 0.209 0.834536
## Congruencyincongruent:Alignmentmisaligned 0.47993 0.06375 7.528 5.15e-14 ***
## Cuebottom:SameDifferentdifferent 0.13278 0.09793 1.356 0.175151
## Congruencyincongruent:SameDifferentdifferent 1.30486 0.11430 11.416 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.29666 0.06509 4.557 5.18e-06 ***
## Cuebottom:Probability2-1 -0.81193 0.20047 -4.050 5.12e-05 ***
## Congruencyincongruent:Probability2-1 0.07495 0.10841 0.691 0.489322
## Alignmentmisaligned:Probability2-1 -0.08376 0.09446 -0.887 0.375222
## SameDifferentdifferent:Probability2-1 -0.80115 0.16663 -4.808 1.52e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.29665 0.09133 -3.248 0.001161 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.17822 0.21033 -0.847 0.396810
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13962 0.09237 -1.512 0.130648
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.74289 0.08870 -8.375 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.32117 0.17589 -1.826 0.067853 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.05622 0.13651 0.412 0.680441
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.12276 0.12730 0.964 0.334893
## Cuebottom:SameDifferentdifferent:Probability2-1 1.39232 0.30536 4.560 5.13e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.17475 0.17314 -1.009 0.312836
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.20194 0.13008 1.552 0.120579
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.56031 0.12553 4.464 8.06e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.14297 0.18228 -0.784 0.432829
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.59909 0.29614 2.023 0.043073 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.17184 0.18454 -0.931 0.351765
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.28785 0.17724 -1.624 0.104364
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.43092 0.25103 1.717 0.086052 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00120721 (tol = 0.001, component 1)file_E2_resp_etd5 <- file.path(folder_lmm, "E2_Resp_lmm_etd5.RData")
# fit the etd5 model
if (!file.exists(file_E2_resp_etd5)) {
ss <- getME(glmm_E2_resp_etd4, c("theta","fixef"))
glmm_E2_resp_etd5 <- update(
glmm_E2_resp_etd4, start=ss,
control=glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
# save(glmm_E2_resp_etd5, file = file_E2_resp_etd5)
} else {
load(file_E2_resp_etd5)
}
print(summary(glmm_E2_resp_etd5), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Cue_Con_Sam + Cue_Pro + Cue_Sam_Pro + Cue_Con_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 42198.4 42603.6 -21052.2 42104.4 40913
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.4599 -0.6086 0.2839 0.5376 4.0135
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5939 0.7706
## Cue_Con_Sam 1.1554 1.0749 0.87
## Cue_Pro 0.4156 0.6447 -0.08 0.03
## Cue_Sam_Pro 2.5695 1.6030 -0.24 -0.18 0.01
## Cue_Con_Sam_Pro 1.7693 1.3301 -0.20 -0.41 -0.10 0.27
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.05176 0.03854 27.292 < 2e-16 ***
## Cuebottom 0.11557 0.06102 1.894 0.058249 .
## Congruencyincongruent -0.80278 0.06508 -12.335 < 2e-16 ***
## Alignmentmisaligned -0.15744 0.04701 -3.349 0.000811 ***
## SameDifferentdifferent -1.89315 0.05884 -32.174 < 2e-16 ***
## Probability2-1 0.48388 0.10960 4.415 1.01e-05 ***
## Cuebottom:Congruencyincongruent 0.06502 0.11415 0.570 0.568940
## Cuebottom:Alignmentmisaligned 0.01428 0.06802 0.210 0.833708
## Congruencyincongruent:Alignmentmisaligned 0.47993 0.06335 7.575 3.59e-14 ***
## Cuebottom:SameDifferentdifferent 0.13278 0.09748 1.362 0.173169
## Congruencyincongruent:SameDifferentdifferent 1.30486 0.11274 11.574 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.29666 0.06459 4.593 4.37e-06 ***
## Cuebottom:Probability2-1 -0.81193 0.19808 -4.099 4.15e-05 ***
## Congruencyincongruent:Probability2-1 0.07495 0.10658 0.703 0.481910
## Alignmentmisaligned:Probability2-1 -0.08376 0.09347 -0.896 0.370187
## SameDifferentdifferent:Probability2-1 -0.80115 0.16416 -4.880 1.06e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.29665 0.09088 -3.264 0.001097 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.17822 0.20761 -0.858 0.390652
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.13962 0.09178 -1.521 0.128201
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.74289 0.08792 -8.449 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.32117 0.17252 -1.862 0.062657 .
## Cuebottom:Alignmentmisaligned:Probability2-1 0.05622 0.13463 0.418 0.676239
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.12276 0.12586 0.975 0.329387
## Cuebottom:SameDifferentdifferent:Probability2-1 1.39232 0.30097 4.626 3.73e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.17475 0.16950 -1.031 0.302554
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.20194 0.12814 1.576 0.115048
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.56031 0.12472 4.492 7.04e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.14297 0.17941 -0.797 0.425519
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.59909 0.28969 2.068 0.038635 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.17184 0.18106 -0.949 0.342595
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.28785 0.17427 -1.652 0.098582 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.43092 0.24538 1.756 0.079067 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.00217891 (tol = 0.001, component 1)summary(rePCA(glmm_E2_resp_etd5))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5]
## Standard deviation 1.7783 1.3185 1.0569 0.64072 0.27414
## Proportion of Variance 0.4862 0.2673 0.1718 0.06312 0.01156
## Cumulative Proportion 0.4862 0.7536 0.9253 0.98844 1.00000Cue_Pro was removed from extended model (glmm_E2_resp_etd5) due to that the variances it explained were smaller than 1%, making glmm_E2_resp_etd6.
file_E2_resp_etd6 <- file.path(folder_lmm, "E2_Resp_lmm_etd6.RData")
# fit the etd6 model
if (!file.exists(file_E2_resp_etd6)) {
glmm_E2_resp_etd6 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
(0 + # Con_C + Ali_C + Cue_C + Sam_C +
Cue_Sam + # Con_Ali + Ali_Sam + Cue_Con + Cue_Ali + Con_Sam +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
# Cue_Con_Ali_Sam +
# Pro_C +
# Con_Pro + Ali_Pro + Sam_Pro + Cue_Pro +
Cue_Sam_Pro + # Ali_Sam_Pro + Cue_Con_Pro + Con_Ali_Pro + Cue_Ali_Pro + Con_Sam_Pro +
Cue_Con_Sam_Pro # Con_Ali_Sam_Pro + Cue_Con_Ali_Pro + Cue_Ali_Sam_Pro + + Cue_Con_Ali_Sam_Pro
| Participant),
family = binomial(link = "probit"),
data = df_lmm_E2,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_resp_etd6, file = file_E2_resp_etd6)
} else {
load(file_E2_resp_etd6)
}
print(summary(glmm_E2_resp_etd6), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (0 + Cue_Sam + Cue_Con_Sam + Cue_Sam_Pro + Cue_Con_Sam_Pro | Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 42628.4 42990.5 -21272.2 42544.4 40918
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3192 -0.6160 0.2881 0.5504 4.1087
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_Sam 0.5961 0.772
## Cue_Con_Sam 1.1423 1.069 0.86
## Cue_Sam_Pro 2.5914 1.610 -0.25 -0.18
## Cue_Con_Sam_Pro 1.8149 1.347 -0.18 -0.41 0.21
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.04400 0.03863 27.029 < 2e-16 ***
## Cuebottom 0.11384 0.06126 1.858 0.063141 .
## Congruencyincongruent -0.79866 0.06513 -12.262 < 2e-16 ***
## Alignmentmisaligned -0.15812 0.04699 -3.365 0.000765 ***
## SameDifferentdifferent -1.87894 0.05919 -31.744 < 2e-16 ***
## Probability2-1 0.46310 0.09769 4.740 2.13e-06 ***
## Cuebottom:Congruencyincongruent 0.06592 0.11428 0.577 0.564029
## Cuebottom:Alignmentmisaligned 0.01625 0.06793 0.239 0.810968
## Congruencyincongruent:Alignmentmisaligned 0.47686 0.06335 7.527 5.19e-14 ***
## Cuebottom:SameDifferentdifferent 0.13508 0.09819 1.376 0.168917
## Congruencyincongruent:SameDifferentdifferent 1.29626 0.11297 11.475 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.29716 0.06466 4.596 4.31e-06 ***
## Cuebottom:Probability2-1 -0.77821 0.17191 -4.527 5.98e-06 ***
## Congruencyincongruent:Probability2-1 0.09082 0.10744 0.845 0.397969
## Alignmentmisaligned:Probability2-1 -0.07939 0.09375 -0.847 0.397053
## SameDifferentdifferent:Probability2-1 -0.77253 0.16871 -4.579 4.67e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.29537 0.09070 -3.257 0.001127 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.17950 0.20809 -0.863 0.388349
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.14209 0.09169 -1.550 0.121211
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.73732 0.08801 -8.377 < 2e-16 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.34341 0.17504 -1.962 0.049775 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.05225 0.13589 0.384 0.700610
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.11591 0.12629 0.918 0.358716
## Cuebottom:SameDifferentdifferent:Probability2-1 1.33920 0.31121 4.303 1.68e-05 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.18728 0.17154 -1.092 0.274955
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.19687 0.12910 1.525 0.127272
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.55742 0.12452 4.476 7.59e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.13464 0.18129 -0.743 0.457684
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.61845 0.29449 2.100 0.035722 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.16449 0.18352 -0.896 0.370076
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.28008 0.17539 -1.597 0.110295
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.41619 0.24859 1.674 0.094092 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00127145 (tol = 0.001, component 1)3.1.1.5 The optimal model
# compare the extended and reduced model
anova(glmm_E2_resp_etd6, glmm_E2_resp_rdc2, refit = FALSE)## Data: df_lmm_E2
## Models:
## glmm_E2_resp_etd6: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
## glmm_E2_resp_etd6: (0 + Cue_Sam + Cue_Con_Sam + Cue_Sam_Pro + Cue_Con_Sam_Pro |
## glmm_E2_resp_etd6: Participant)
## glmm_E2_resp_rdc2: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability +
## glmm_E2_resp_rdc2: (Cue_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam +
## glmm_E2_resp_rdc2: Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro +
## glmm_E2_resp_rdc2: Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro +
## glmm_E2_resp_rdc2: Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_E2_resp_etd6 42 42628 42990 -21272 42544
## glmm_E2_resp_rdc2 50 39575 40006 -19738 39475 3069.2 8 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to BIC, the reduced model (glmm_E2_resp_rdc2) explained the data better than the extended model (glmm_resp_etd4) and, therefore, the reduced model is used as the optimal model.
glmm_E2_resp_opt <- glmm_E2_resp_rdc2
print(summary(glmm_E2_resp_opt), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent * Probability + (Cue_C + Sam_C + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam + Pro_C + Cue_Pro + Sam_Pro + Cue_Ali_Pro + Cue_Sam_Pro + Con_Sam_Pro + Cue_Con_Sam_Pro + Cue_Ali_Sam_Pro + Cue_Con_Ali_Sam_Pro || Participant)
## Data: df_lmm_E2
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 39575.2 40006.3 -19737.6 39475.2 40910
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.6455 -0.5528 0.1967 0.5113 5.7139
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.07145 0.2673
## Participant.1 Cue_C 0.12947 0.3598
## Participant.2 Sam_C 0.19931 0.4464
## Participant.3 Cue_Ali 0.04192 0.2047
## Participant.4 Cue_Sam 0.58683 0.7660
## Participant.5 Con_Sam 0.38364 0.6194
## Participant.6 Cue_Con_Sam 1.15766 1.0759
## Participant.7 Con_Ali_Sam 0.10035 0.3168
## Participant.8 Cue_Con_Ali_Sam 0.07774 0.2788
## Participant.9 Pro_C 0.05713 0.2390
## Participant.10 Cue_Pro 0.40833 0.6390
## Participant.11 Sam_Pro 0.04196 0.2048
## Participant.12 Cue_Ali_Pro 0.10085 0.3176
## Participant.13 Cue_Sam_Pro 1.54889 1.2445
## Participant.14 Con_Sam_Pro 0.12625 0.3553
## Participant.15 Cue_Con_Sam_Pro 2.48434 1.5762
## Participant.16 Cue_Ali_Sam_Pro 0.08956 0.2993
## Participant.17 Cue_Con_Ali_Sam_Pro 0.09184 0.3030
## Number of obs: 40960, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.164756 0.093859 12.410 < 2e-16 ***
## Cuebottom 0.133595 0.119396 1.119 0.26317
## Congruencyincongruent -0.919451 0.088659 -10.371 < 2e-16 ***
## Alignmentmisaligned -0.175552 0.056182 -3.125 0.00178 **
## SameDifferentdifferent -2.082488 0.137486 -15.147 < 2e-16 ***
## Probability2-1 0.504191 0.124335 4.055 5.01e-05 ***
## Cuebottom:Congruencyincongruent 0.082452 0.119261 0.691 0.48934
## Cuebottom:Alignmentmisaligned -0.002788 0.083158 -0.034 0.97325
## Congruencyincongruent:Alignmentmisaligned 0.535632 0.074313 7.208 5.69e-13 ***
## Cuebottom:SameDifferentdifferent 0.144981 0.180905 0.801 0.42289
## Congruencyincongruent:SameDifferentdifferent 1.484362 0.162668 9.125 < 2e-16 ***
## Alignmentmisaligned:SameDifferentdifferent 0.327358 0.075751 4.322 1.55e-05 ***
## Cuebottom:Probability2-1 -0.800391 0.204913 -3.906 9.38e-05 ***
## Congruencyincongruent:Probability2-1 0.113429 0.123145 0.921 0.35699
## Alignmentmisaligned:Probability2-1 -0.071931 0.106629 -0.675 0.49994
## SameDifferentdifferent:Probability2-1 -0.786107 0.171382 -4.587 4.50e-06 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -0.319841 0.100426 -3.185 0.00145 **
## Cuebottom:Congruencyincongruent:SameDifferentdifferent -0.226218 0.214466 -1.055 0.29152
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent -0.126699 0.101285 -1.251 0.21097
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent -0.820362 0.111485 -7.358 1.86e-13 ***
## Cuebottom:Congruencyincongruent:Probability2-1 -0.441981 0.197312 -2.240 0.02509 *
## Cuebottom:Alignmentmisaligned:Probability2-1 0.041045 0.160452 0.256 0.79810
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 0.120043 0.136301 0.881 0.37847
## Cuebottom:SameDifferentdifferent:Probability2-1 1.351061 0.297076 4.548 5.42e-06 ***
## Congruencyincongruent:SameDifferentdifferent:Probability2-1 -0.270287 0.202271 -1.336 0.18146
## Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.179901 0.141997 1.267 0.20518
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent 0.601164 0.140948 4.265 2.00e-05 ***
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -0.134248 0.196907 -0.682 0.49538
## Cuebottom:Congruencyincongruent:SameDifferentdifferent:Probability2-1 0.790854 0.336433 2.351 0.01874 *
## Cuebottom:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.144169 0.205911 -0.700 0.48383
## Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 -0.284773 0.188893 -1.508 0.13166
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:SameDifferentdifferent:Probability2-1 0.426096 0.270915 1.573 0.11576
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.1.2 Estimated marginal means
3.1.2.1 Estimated marginal means for hit and false alarm
(emm_E2_resp <- emmeans(glmm_E2_resp_opt, ~ Alignment + Congruency + Cue + SameDifferent + Probability))## Alignment Congruency Cue SameDifferent Probability emmean SE df asymp.LCL asymp.UCL
## aligned congruent top same 0.25 0.9127 0.116 Inf 0.6844 1.1409
## misaligned congruent top same 0.25 0.7731 0.116 Inf 0.5464 0.9997
## aligned incongruent top same 0.25 -0.0635 0.113 Inf -0.2850 0.1580
## misaligned incongruent top same 0.25 0.2725 0.113 Inf 0.0501 0.4950
## aligned congruent bottom same 0.25 1.4465 0.109 Inf 1.2332 1.6597
## misaligned congruent bottom same 0.25 1.2836 0.107 Inf 1.0730 1.4941
## aligned incongruent bottom same 0.25 0.7737 0.106 Inf 0.5669 0.9805
## misaligned incongruent bottom same 0.25 0.8337 0.106 Inf 0.6264 1.0411
## aligned congruent top different 0.25 -0.7768 0.115 Inf -1.0027 -0.5508
## misaligned congruent top different 0.25 -0.6790 0.115 Inf -0.9035 -0.4544
## aligned incongruent top different 0.25 -0.1334 0.113 Inf -0.3543 0.0874
## misaligned incongruent top different 0.25 -0.2380 0.113 Inf -0.4589 -0.0171
## aligned congruent bottom different 0.25 -0.7735 0.105 Inf -0.9795 -0.5675
## misaligned congruent bottom different 0.25 -0.7536 0.105 Inf -0.9594 -0.5478
## aligned incongruent bottom different 0.25 -0.4484 0.105 Inf -0.6532 -0.2435
## misaligned incongruent bottom different 0.25 -0.4955 0.105 Inf -0.7004 -0.2906
## aligned congruent top same 0.75 1.4169 0.109 Inf 1.2041 1.6296
## misaligned congruent top same 0.75 1.2053 0.107 Inf 0.9955 1.4152
## aligned incongruent top same 0.75 0.5541 0.105 Inf 0.3492 0.7590
## misaligned incongruent top same 0.75 0.9383 0.106 Inf 0.7308 1.1457
## aligned congruent bottom same 0.75 1.1503 0.119 Inf 0.9166 1.3839
## misaligned congruent bottom same 0.75 0.9565 0.117 Inf 0.7274 1.1855
## aligned incongruent bottom same 0.75 0.1490 0.113 Inf -0.0728 0.3707
## misaligned incongruent bottom same 0.75 0.1639 0.113 Inf -0.0579 0.3857
## aligned congruent top different 0.75 -1.0587 0.106 Inf -1.2664 -0.8510
## misaligned congruent top different 0.75 -0.8529 0.105 Inf -1.0590 -0.6468
## aligned incongruent top different 0.75 -0.5722 0.105 Inf -0.7771 -0.3673
## misaligned incongruent top different 0.75 -0.7335 0.105 Inf -0.9392 -0.5278
## aligned congruent bottom different 0.75 -0.5048 0.113 Inf -0.7269 -0.2826
## misaligned congruent bottom different 0.75 -0.4800 0.113 Inf -0.7016 -0.2585
## aligned incongruent bottom different 0.75 0.0124 0.112 Inf -0.2081 0.2329
## misaligned incongruent bottom different 0.75 0.0973 0.113 Inf -0.1235 0.3180
##
## Results are given on the probit (not the response) scale.
## Confidence level used: 0.953.1.2.2 Estimated marginal means for d’
emm_E2_d <- contrast(emm_E2_resp, method = "pairwise", simple = "SameDifferent")
summary(emm_E2_d[1:16], infer = c(TRUE, FALSE), adjust = "none")## contrast Alignment Congruency Cue Probability estimate SE df asymp.LCL asymp.UCL
## same - different aligned congruent top 0.25 1.6894 0.168 Inf 1.361 2.018
## same - different misaligned congruent top 0.25 1.4520 0.167 Inf 1.125 1.779
## same - different aligned incongruent top 0.25 0.0699 0.164 Inf -0.251 0.391
## same - different misaligned incongruent top 0.25 0.5105 0.164 Inf 0.189 0.832
## same - different aligned congruent bottom 0.25 2.2200 0.156 Inf 1.915 2.525
## same - different misaligned congruent bottom 0.25 2.0372 0.155 Inf 1.734 2.340
## same - different aligned incongruent bottom 0.25 1.2221 0.153 Inf 0.922 1.522
## same - different misaligned incongruent bottom 0.25 1.3292 0.153 Inf 1.029 1.629
## same - different aligned congruent top 0.75 2.4755 0.156 Inf 2.170 2.781
## same - different misaligned congruent top 0.75 2.0582 0.154 Inf 1.756 2.361
## same - different aligned incongruent top 0.75 1.1263 0.152 Inf 0.828 1.425
## same - different misaligned incongruent top 0.75 1.6718 0.154 Inf 1.371 1.973
## same - different aligned congruent bottom 0.75 1.6550 0.169 Inf 1.325 1.985
## same - different misaligned congruent bottom 0.75 1.4365 0.167 Inf 1.110 1.763
## same - different aligned incongruent bottom 0.75 0.1366 0.164 Inf -0.184 0.458
## same - different misaligned incongruent bottom 0.75 0.0666 0.164 Inf -0.254 0.388
##
## Note: contrasts are still on the probit scale
## Confidence level used: 0.95# emmip(emm_E2_d, Congruency ~ Alignment | Cue + Probability, CIs = TRUE)plot_E2_cf_d <- summary(emm_E2_d[1:16], infer = c(TRUE, FALSE), adjust = "sidak") %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(Probability ~Cue, switch = "x",
labeller = labeller(Probability = c(`0.25` = "25% cueing top", `0.75` = "75% cueing top"))) +
coord_cartesian(ylim = ylimit_cf_d) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = expression("Sensitivity"~italic("d'")), fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("***", "", "", "", "*", "", "", "", "***", "", "", "", "", "", "", ""), color = "red", size = 6, nudge_y = 0.4, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E2_cf_d.pdf", plot_E2_cf_d, width = 8, height = 4.8)
plot_E2_cf_d
3.1.2.3 Composite effects
Composite face effects for top and bottom parts:
emm_E2_d_cf <- contrast(emm_E2_resp, interaction = "pairwise", by = c("Cue", "Probability"))
summary(emm_E2_d_cf[1:4], infer = TRUE)## Alignment_pairwise Congruency_pairwise SameDifferent_pairwise Cue Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned congruent - incongruent same - different top 0.25 0.678 0.170 Inf 0.3457 1.010 4.000 0.0001
## aligned - misaligned congruent - incongruent same - different bottom 0.25 0.290 0.118 Inf 0.0584 0.521 2.455 0.0141
## aligned - misaligned congruent - incongruent same - different top 0.75 0.963 0.118 Inf 0.7311 1.194 8.147 <.0001
## aligned - misaligned congruent - incongruent same - different bottom 0.75 0.149 0.170 Inf -0.1852 0.482 0.872 0.3830
##
## Confidence level used: 0.95emm_E2_d_con <- contrast(emm_E2_resp, interaction = "pairwise", by = c("Cue", "Probability", "Alignment"))
summary(emm_E2_d_con[seq(1,7,2)], infer = TRUE)## Congruency_pairwise SameDifferent_pairwise Cue Probability Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent same - different top 0.25 aligned 1.620 0.201 Inf 1.226 2.01 8.063 <.0001
## congruent - incongruent same - different bottom 0.25 aligned 0.998 0.182 Inf 0.641 1.35 5.483 <.0001
## congruent - incongruent same - different top 0.75 aligned 1.349 0.182 Inf 0.993 1.71 7.423 <.0001
## congruent - incongruent same - different bottom 0.75 aligned 1.518 0.202 Inf 1.123 1.91 7.525 <.0001
##
## Confidence level used: 0.953.1.2.4 Facilitation and interference
# Sensitivity d'
emm_E2_d_fi <- contrast(emm_E2_resp, interaction = "pairwise", by = c("Cue", "Congruency", "Probability"), adjust = "sidak")
summary(emm_E2_d_fi[1:8], infer=TRUE)## Alignment_pairwise SameDifferent_pairwise Cue Congruency Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned same - different top congruent 0.25 0.237 0.1211 Inf -0.0928 0.568 1.961 0.3360
## aligned - misaligned same - different top incongruent 0.25 -0.441 0.1116 Inf -0.7449 -0.136 -3.948 0.0006
## aligned - misaligned same - different bottom congruent 0.25 0.183 0.0824 Inf -0.0420 0.408 2.217 0.1940
## aligned - misaligned same - different bottom incongruent 0.25 -0.107 0.0748 Inf -0.3112 0.097 -1.431 0.7340
## aligned - misaligned same - different top congruent 0.75 0.417 0.0831 Inf 0.1908 0.644 5.024 <.0001
## aligned - misaligned same - different top incongruent 0.75 -0.545 0.0742 Inf -0.7478 -0.343 -7.350 <.0001
## aligned - misaligned same - different bottom congruent 0.75 0.219 0.1221 Inf -0.1143 0.551 1.790 0.4567
## aligned - misaligned same - different bottom incongruent 0.75 0.070 0.1115 Inf -0.2340 0.374 0.628 0.9976
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 8 estimates
## P value adjustment: sidak method for 8 tests# emmip(emm_E2_d_fi[1:8], ~ Probability | Cue + Congruency, CIs = TRUE, adjust = "sidak")plot_E2_cffi_d <- summary(emm_E2_d_fi[1:8], infer=TRUE) %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(Probability ~ Congruency, switch = "x",
labeller = labeller(Probability = c(`0.25` = "25% cueing top", `0.75` = "75% cueing top"))) +
coord_cartesian(ylim = ylimit_cf_fi_d) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(italic("d'")~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E2_fi_d.pdf", plot_E2_cffi_d, width = 7, height = 4.55)
plot_E2_cffi_d
plot_E2_cf_d_ <- plot_E2_cf_d +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.6, 0.5),
legend.box = "horizontal")
plot_E2_d <- ggarrange(plot_E2_cf_d_, plot_E2_cffi_d,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E2_d.pdf", plot_E2_d, width = 10, height = 7)
plot_E2_d
3.1.2.5 Comparisons between facilitation and interference
contrast(emm_E2_d_fi, method = list("faci-inte"=c(1, 1)), by = c("Cue", "Probability"))[1:4] %>%
summary(infer = TRUE)## contrast Cue Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top 0.25 -0.2032 0.160 Inf -0.5161 0.110 -1.272 0.2032
## faci-inte bottom 0.25 0.0757 0.104 Inf -0.1284 0.280 0.727 0.4672
## faci-inte top 0.75 -0.1281 0.104 Inf -0.3323 0.076 -1.230 0.2186
## faci-inte bottom 0.75 0.2885 0.160 Inf -0.0254 0.602 1.801 0.0716
##
## Confidence level used: 0.953.2 Response times
df_lmm_E2_rt <- df_lmm_E2 %>%
filter(isCorrect == 1)
# save(df_lmm_E2_rt, file = file.path("data", "df_lmm_E2_rt.RData"))3.2.1 Fitting the generalized mixed models
with log-transformation. #### The maximal model
# file_E2_rt_max <- file.path(folder_lmm, "E2_rt_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_E2_rt_max)) {
# glmm_E2_rt_max <- glmer(
# log(RT) ~ Cue * Congruency * Alignment * Probability +
# (Cue * Congruency * Alignment * Probability | Participant),
# family = lognormal(),
# data = df_lmm_rt,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_E2_rt_max, file = file_E2_rt_max)
# } else {
# load(file_E2_rt_max)
# }
#
# print(summary(glmm_E2_rt_max), corr = FALSE)3.2.1.1 The zero-correlation-parameter model
file_E2_rt_zcp <- file.path(folder_lmm, "E2_rt_lmm_zcp.RData")
# fit the zcp1 model
if (!file.exists(file_E2_rt_zcp)) {
glmm_E2_rt_zcp <- lmer(
log(RT) ~ Cue * Congruency * Alignment * Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + Cue_Ali + Con_Ali +
Cue_Con_Ali +
Pro_C +
Cue_Pro + Con_Pro + Ali_Pro +
Cue_Con_Pro + Cue_Ali_Pro + Con_Ali_Pro +
Cue_Con_Ali_Pro || Participant),
data = df_lmm_E2_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_rt_zcp, file = file_E2_rt_zcp)
} else {
load(file_E2_rt_zcp)
}
print(summary(glmm_E2_rt_zcp), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Con_Ali + Cue_Con_Ali + Pro_C + Cue_Pro + Con_Pro + Ali_Pro + Cue_Con_Pro + Cue_Ali_Pro + Con_Ali_Pro + Cue_Con_Ali_Pro || Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20092.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2443 -0.5901 -0.1322 0.4296 10.6198
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 4.570e-02 2.138e-01
## Participant.1 Cue_C 4.814e-03 6.938e-02
## Participant.2 Con_C 3.427e-04 1.851e-02
## Participant.3 Ali_C 5.044e-04 2.246e-02
## Participant.4 Cue_Con 6.945e-04 2.635e-02
## Participant.5 Cue_Ali 0.000e+00 0.000e+00
## Participant.6 Con_Ali 5.039e-04 2.245e-02
## Participant.7 Cue_Con_Ali 2.215e-04 1.488e-02
## Participant.8 Pro_C 4.729e-02 2.175e-01
## Participant.9 Cue_Pro 7.550e-02 2.748e-01
## Participant.10 Con_Pro 5.963e-10 2.442e-05
## Participant.11 Ali_Pro 0.000e+00 0.000e+00
## Participant.12 Cue_Con_Pro 4.505e-09 6.712e-05
## Participant.13 Cue_Ali_Pro 4.565e-03 6.756e-02
## Participant.14 Con_Ali_Pro 0.000e+00 0.000e+00
## Participant.15 Cue_Con_Ali_Pro 2.012e-07 4.485e-04
## Residual 1.110e-01 3.331e-01
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.690e+00 3.888e-02 3.443e+01 172.052 < 2e-16 ***
## Cuebottom -3.155e-03 1.519e-02 5.423e+01 -0.208 0.836273
## Congruencyincongruent 6.257e-02 1.055e-02 2.057e+02 5.928 1.28e-08 ***
## Alignmentmisaligned 4.145e-02 9.755e-03 1.622e+02 4.249 3.61e-05 ***
## Probability2-1 -1.247e-01 4.716e-02 5.844e+01 -2.645 0.010470 *
## Cuebottom:Congruencyincongruent 1.630e-02 1.434e-02 1.077e+02 1.136 0.258321
## Cuebottom:Alignmentmisaligned 5.224e-03 1.236e-02 1.623e+02 0.423 0.672997
## Congruencyincongruent:Alignmentmisaligned -4.881e-02 1.387e-02 1.121e+02 -3.520 0.000625 ***
## Cuebottom:Probability2-1 2.721e-01 5.190e-02 3.737e+01 5.244 6.46e-06 ***
## Congruencyincongruent:Probability2-1 -4.404e-02 1.904e-02 2.999e+04 -2.312 0.020776 *
## Alignmentmisaligned:Probability2-1 -3.556e-02 1.832e-02 2.877e+02 -1.941 0.053234 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -1.675e-03 1.906e-02 5.759e+01 -0.088 0.930264
## Cuebottom:Congruencyincongruent:Probability2-1 7.721e-02 2.697e-02 2.933e+04 2.863 0.004201 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.364e-02 2.734e-02 8.972e+01 3.059 0.002927 **
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.539e-02 2.643e-02 2.927e+04 1.718 0.085855 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.483e-02 3.773e-02 2.709e+04 -1.453 0.146240
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingular3.2.1.2 The reduced model
summary(rePCA(glmm_E2_rt_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
## Standard deviation 0.8248 0.6528 0.6418 0.20828 0.20281 0.07911 0.06742 0.06739 0.05557 0.04468 0.001346 0.0002015 7.33e-05 0 0 0
## Proportion of Variance 0.4191 0.2625 0.2537 0.02673 0.02534 0.00386 0.00280 0.00280 0.00190 0.00123 0.000000 0.0000000 0.00e+00 0 0 0
## Cumulative Proportion 0.4191 0.6816 0.9354 0.96207 0.98741 0.99127 0.99407 0.99687 0.99877 1.00000 1.000000 1.0000000 1.00e+00 1 1 1Cue_Ali, Ali_Pro, Con_Ali_Pro, Con_Pro, Cue_Con_Pro, and Cue_Con_Ali_Pro were removed from extended model (glmm_E2_rt_zcp) due to that the variance it explained was smaller than 0.1%, making glmm_E2_rt_rdc.
file_E2_rt_rdc <- file.path(folder_lmm, "E2_rt_lmm_rdc.RData")
# fit the rdc1 model
if (!file.exists(file_E2_rt_rdc)) {
glmm_E2_rt_rdc <- lmer(
log(RT) ~ Cue * Congruency * Alignment * Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + Con_Ali + # Cue_Ali +
Cue_Con_Ali +
Pro_C +
Cue_Pro + # Ali_Pro + Con_Pro +
Cue_Ali_Pro # Con_Ali_Pro + Cue_Con_Pro +
|| Participant), # Cue_Con_Ali_Pro
data = df_lmm_E2_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_rt_rdc, file = file_E2_rt_rdc)
} else {
load(file_E2_rt_rdc)
}
print(summary(glmm_E2_rt_rdc), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Con_Ali + Cue_Con_Ali + Pro_C + Cue_Pro + Cue_Ali_Pro || Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20092.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2444 -0.5901 -0.1322 0.4295 10.6198
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0457251 0.21383
## Participant.1 Cue_C 0.0048160 0.06940
## Participant.2 Con_C 0.0003423 0.01850
## Participant.3 Ali_C 0.0005045 0.02246
## Participant.4 Cue_Con 0.0006969 0.02640
## Participant.5 Con_Ali 0.0005035 0.02244
## Participant.6 Cue_Con_Ali 0.0002217 0.01489
## Participant.7 Pro_C 0.0473011 0.21749
## Participant.8 Cue_Pro 0.0754976 0.27477
## Participant.9 Cue_Ali_Pro 0.0045724 0.06762
## Residual 0.1109745 0.33313
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.690e+00 3.889e-02 3.441e+01 172.015 < 2e-16 ***
## Cuebottom -3.155e-03 1.519e-02 5.420e+01 -0.208 0.836278
## Congruencyincongruent 6.257e-02 1.056e-02 2.057e+02 5.928 1.28e-08 ***
## Alignmentmisaligned 4.145e-02 9.755e-03 1.622e+02 4.249 3.61e-05 ***
## Probability2-1 -1.247e-01 4.716e-02 5.842e+01 -2.645 0.010478 *
## Cuebottom:Congruencyincongruent 1.630e-02 1.434e-02 1.077e+02 1.136 0.258371
## Cuebottom:Alignmentmisaligned 5.224e-03 1.236e-02 1.623e+02 0.423 0.673007
## Congruencyincongruent:Alignmentmisaligned -4.881e-02 1.387e-02 1.121e+02 -3.520 0.000624 ***
## Cuebottom:Probability2-1 2.721e-01 5.190e-02 3.737e+01 5.244 6.46e-06 ***
## Congruencyincongruent:Probability2-1 -4.404e-02 1.904e-02 3.018e+04 -2.312 0.020775 *
## Alignmentmisaligned:Probability2-1 -3.556e-02 1.832e-02 2.874e+02 -1.941 0.053255 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -1.675e-03 1.906e-02 5.760e+01 -0.088 0.930246
## Cuebottom:Congruencyincongruent:Probability2-1 7.721e-02 2.697e-02 3.008e+04 2.863 0.004201 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.364e-02 2.735e-02 8.966e+01 3.059 0.002932 **
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.539e-02 2.643e-02 2.998e+04 1.718 0.085863 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.483e-02 3.773e-02 2.956e+04 -1.453 0.146248
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.2.1.3 The extended model
file_E2_rt_etd <- file.path(folder_lmm, "E2_rt_lmm_etd.RData")
# fit the etd model
if (!file.exists(file_E2_rt_etd)) {
glmm_E2_rt_etd <- lmer(
log(RT) ~ Cue * Congruency * Alignment * Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + Con_Ali + # Cue_Ali +
Cue_Con_Ali +
Pro_C +
Cue_Pro + # Ali_Pro + Con_Pro +
Cue_Ali_Pro # Con_Ali_Pro + Cue_Con_Pro +
| Participant), # Cue_Con_Ali_Pro
data = df_lmm_E2_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_rt_etd, file = file_E2_rt_etd)
} else {
load(file_E2_rt_etd)
}
print(summary(glmm_E2_rt_etd), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Con_Ali + Cue_Con_Ali + Pro_C + Cue_Pro + Cue_Ali_Pro | Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20010.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2586 -0.5908 -0.1304 0.4305 10.6496
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0464276 0.21547
## Cue_C 0.0049674 0.07048 -0.20
## Con_C 0.0004322 0.02079 0.33 -0.46
## Ali_C 0.0007474 0.02734 0.17 0.16 0.06
## Cue_Con 0.0010951 0.03309 0.01 0.38 -0.32 -0.26
## Con_Ali 0.0012791 0.03576 -0.09 0.02 -0.48 -0.08 0.44
## Cue_Con_Ali 0.0039599 0.06293 -0.63 0.07 -0.10 -0.55 -0.12 0.29
## Pro_C 0.0479580 0.21899 0.09 0.30 -0.72 0.07 0.42 0.21 -0.48
## Cue_Pro 0.0763459 0.27631 0.53 -0.24 0.20 -0.38 0.02 -0.58 -0.47 0.23
## Cue_Ali_Pro 0.0089737 0.09473 -0.15 0.30 -0.16 0.36 -0.35 0.29 0.25 0.06 -0.61
## Residual 0.1107688 0.33282
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.690e+00 4.013e-02 3.103e+01 166.699 < 2e-16 ***
## Cuebottom -2.038e-03 1.501e-02 4.127e+01 -0.136 0.89266
## Congruencyincongruent 6.184e-02 1.232e-02 5.877e+01 5.021 5.08e-06 ***
## Alignmentmisaligned 4.106e-02 9.936e-03 8.377e+01 4.132 8.48e-05 ***
## Probability2-1 -1.244e-01 4.429e-02 3.361e+01 -2.810 0.00821 **
## Cuebottom:Congruencyincongruent 1.510e-02 1.596e-02 6.841e+01 0.946 0.34754
## Cuebottom:Alignmentmisaligned 3.857e-03 1.348e-02 1.917e+02 0.286 0.77504
## Congruencyincongruent:Alignmentmisaligned -4.682e-02 1.499e-02 1.019e+02 -3.123 0.00233 **
## Cuebottom:Probability2-1 2.716e-01 5.702e-02 3.326e+01 4.764 3.63e-05 ***
## Congruencyincongruent:Probability2-1 -4.329e-02 1.904e-02 2.979e+04 -2.274 0.02300 *
## Alignmentmisaligned:Probability2-1 -3.545e-02 1.922e-02 2.027e+02 -1.844 0.06661 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -1.385e-04 2.186e-02 8.332e+01 -0.006 0.99496
## Cuebottom:Congruencyincongruent:Probability2-1 7.713e-02 2.695e-02 2.985e+04 2.862 0.00422 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.401e-02 2.974e-02 7.293e+01 2.825 0.00610 **
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.266e-02 2.640e-02 2.988e+04 1.616 0.10612
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.287e-02 3.767e-02 2.964e+04 -1.404 0.16046
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E2_rt_etd))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## Standard deviation 0.9715 0.6509 0.5085 0.21791 0.18936 0.14860 0.05757 0.01157 0.001596 1.485e-05
## Proportion of Variance 0.5440 0.2442 0.1490 0.02737 0.02067 0.01273 0.00191 0.00008 0.000000 0.000e+00
## Cumulative Proportion 0.5440 0.7882 0.9373 0.96462 0.98528 0.99801 0.99992 1.00000 1.000000 1.000e+00Con_C, Ali_C, Cue_C, and Cue_Ali_Pro were removed from extended model.
file_E2_rt_etd1 <- file.path(folder_lmm, "E2_rt_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_E2_rt_etd1)) {
glmm_E2_rt_etd1 <- lmer(
log(RT) ~ Cue * Congruency * Alignment * Probability +
( # Cue_C + Con_C + Ali_C +
Cue_Con + Con_Ali + # Cue_Ali +
Cue_Con_Ali +
Pro_C +
Cue_Pro # Ali_Pro + Con_Pro +
# Con_Ali_Pro + Cue_Con_Pro + Cue_Ali_Pro
| Participant), # Cue_Con_Ali_Pro
data = df_lmm_E2_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_rt_etd1, file = file_E2_rt_etd1)
} else {
load(file_E2_rt_etd1)
}
print(summary(glmm_E2_rt_etd1), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_Con + Con_Ali + Cue_Con_Ali + Pro_C + Cue_Pro | Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20233.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1945 -0.5956 -0.1291 0.4333 10.5434
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0460165 0.21451
## Cue_Con 0.0006146 0.02479 0.07
## Con_Ali 0.0007873 0.02806 -0.14 0.65
## Cue_Con_Ali 0.0023819 0.04880 -0.81 -0.09 0.08
## Pro_C 0.0444586 0.21085 0.15 0.51 0.29 -0.64
## Cue_Pro 0.0761836 0.27601 0.53 0.10 -0.64 -0.54 0.31
## Residual 0.1120021 0.33467
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.688e+00 3.923e-02 3.182e+01 170.466 < 2e-16 ***
## Cuebottom -1.585e-03 9.221e-03 2.488e+02 -0.172 0.863640
## Congruencyincongruent 6.336e-02 1.065e-02 1.165e+02 5.949 2.90e-08 ***
## Alignmentmisaligned 4.267e-02 9.245e-03 3.125e+02 4.615 5.74e-06 ***
## Probability2-1 -1.217e-01 3.961e-02 3.589e+01 -3.074 0.004026 **
## Cuebottom:Congruencyincongruent 1.544e-02 1.492e-02 1.070e+02 1.035 0.302881
## Cuebottom:Alignmentmisaligned 4.047e-03 1.307e-02 3.146e+02 0.310 0.756947
## Congruencyincongruent:Alignmentmisaligned -5.010e-02 1.467e-02 1.245e+02 -3.414 0.000865 ***
## Cuebottom:Probability2-1 2.693e-01 5.178e-02 3.643e+01 5.202 7.85e-06 ***
## Congruencyincongruent:Probability2-1 -4.602e-02 1.906e-02 3.022e+04 -2.415 0.015755 *
## Alignmentmisaligned:Probability2-1 -3.711e-02 1.738e-02 3.024e+04 -2.135 0.032752 *
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -1.388e-05 2.078e-02 1.263e+02 -0.001 0.999468
## Cuebottom:Congruencyincongruent:Probability2-1 8.156e-02 2.700e-02 3.026e+04 3.021 0.002523 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.534e-02 2.466e-02 3.024e+04 3.460 0.000540 ***
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.671e-02 2.650e-02 3.023e+04 1.763 0.077914 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.904e-02 3.781e-02 3.018e+04 -1.562 0.118375
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_E2_rt_etd1))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6]
## Standard deviation 0.9621 0.5960 0.4831 0.08617 6.331e-06 4.056e-06
## Proportion of Variance 0.6083 0.2334 0.1534 0.00488 0.000e+00 0.000e+00
## Cumulative Proportion 0.6083 0.8417 0.9951 1.00000 1.000e+00 1.000e+00Cue_Con, Con_Ali, and Cue_Con_Ali were removed from extended model.
file_E2_rt_etd2 <- file.path(folder_lmm, "E2_rt_lmm_etd2.RData")
# fit the etd2 model
if (!file.exists(file_E2_rt_etd2)) {
glmm_E2_rt_etd2 <- lmer(
log(RT) ~ Cue * Congruency * Alignment * Probability +
( # Cue_C + Con_C + Ali_C +
# Cue_Ali + Con_Ali + Cue_Con +
# Cue_Con_Ali +
Pro_C +
Cue_Pro # Ali_Pro + Con_Pro +
# Con_Ali_Pro + Cue_Con_Pro + Cue_Ali_Pro
| Participant), # Cue_Con_Ali_Pro
data = df_lmm_E2_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_E2_rt_etd2, file = file_E2_rt_etd2)
} else {
load(file_E2_rt_etd2)
}
print(summary(glmm_E2_rt_etd2), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Pro_C + Cue_Pro | Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20255.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1850 -0.5961 -0.1295 0.4324 10.5556
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.04609 0.2147
## Pro_C 0.04458 0.2111 0.15
## Cue_Pro 0.07626 0.2761 0.53 0.31
## Residual 0.11212 0.3348
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.688e+00 3.844e-02 3.234e+01 173.996 < 2e-16 ***
## Cuebottom -1.724e-03 8.648e-03 3.027e+04 -0.199 0.842035
## Congruencyincongruent 6.324e-02 9.525e-03 3.028e+04 6.639 3.20e-11 ***
## Alignmentmisaligned 4.252e-02 8.694e-03 3.026e+04 4.891 1.01e-06 ***
## Probability2-1 -1.222e-01 3.967e-02 3.588e+01 -3.080 0.003958 **
## Cuebottom:Congruencyincongruent 1.640e-02 1.347e-02 3.027e+04 1.218 0.223357
## Cuebottom:Alignmentmisaligned 4.951e-03 1.234e-02 3.026e+04 0.401 0.688210
## Congruencyincongruent:Alignmentmisaligned -5.016e-02 1.325e-02 3.027e+04 -3.785 0.000154 ***
## Cuebottom:Probability2-1 2.705e-01 5.180e-02 3.644e+01 5.222 7.38e-06 ***
## Congruencyincongruent:Probability2-1 -4.541e-02 1.906e-02 3.028e+04 -2.382 0.017220 *
## Alignmentmisaligned:Probability2-1 -3.658e-02 1.739e-02 3.026e+04 -2.104 0.035388 *
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -2.584e-03 1.891e-02 3.026e+04 -0.137 0.891276
## Cuebottom:Congruencyincongruent:Probability2-1 7.937e-02 2.701e-02 3.028e+04 2.939 0.003300 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.363e-02 2.467e-02 3.026e+04 3.389 0.000702 ***
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.645e-02 2.651e-02 3.027e+04 1.752 0.079722 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.607e-02 3.782e-02 3.027e+04 -1.483 0.138190
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.2.1.4 The optimal model
# compare the extended and reduced model
anova(glmm_E2_rt_etd2, glmm_E2_rt_rdc, refit = FALSE)## Data: df_lmm_E2_rt
## Models:
## glmm_E2_rt_etd2: log(RT) ~ Cue * Congruency * Alignment * Probability + (Pro_C +
## glmm_E2_rt_etd2: Cue_Pro | Participant)
## glmm_E2_rt_rdc: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_C +
## glmm_E2_rt_rdc: Con_C + Ali_C + Cue_Con + Con_Ali + Cue_Con_Ali + Pro_C +
## glmm_E2_rt_rdc: Cue_Pro + Cue_Ali_Pro || Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_E2_rt_etd2 23 20301 20493 -10128 20255
## glmm_E2_rt_rdc 27 20146 20371 -10046 20092 162.98 4 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to BIC, the reduced model (glmm_E2_rt_rdc) explained the data better than the extended model (glmm_E2_rt_etd1) and, therefore, the reduced model is used as the optimal model.
glmm_E2_rt_opt <- glmm_E2_rt_rdc
print(summary(glmm_E2_rt_opt), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment * Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Con_Ali + Cue_Con_Ali + Pro_C + Cue_Pro + Cue_Ali_Pro || Participant)
## Data: df_lmm_E2_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 20092.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2444 -0.5901 -0.1322 0.4295 10.6198
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0457251 0.21383
## Participant.1 Cue_C 0.0048160 0.06940
## Participant.2 Con_C 0.0003423 0.01850
## Participant.3 Ali_C 0.0005045 0.02246
## Participant.4 Cue_Con 0.0006969 0.02640
## Participant.5 Con_Ali 0.0005035 0.02244
## Participant.6 Cue_Con_Ali 0.0002217 0.01489
## Participant.7 Pro_C 0.0473011 0.21749
## Participant.8 Cue_Pro 0.0754976 0.27477
## Participant.9 Cue_Ali_Pro 0.0045724 0.06762
## Residual 0.1109745 0.33313
## Number of obs: 30371, groups: Participant, 32
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.690e+00 3.889e-02 3.441e+01 172.015 < 2e-16 ***
## Cuebottom -3.155e-03 1.519e-02 5.420e+01 -0.208 0.836278
## Congruencyincongruent 6.257e-02 1.056e-02 2.057e+02 5.928 1.28e-08 ***
## Alignmentmisaligned 4.145e-02 9.755e-03 1.622e+02 4.249 3.61e-05 ***
## Probability2-1 -1.247e-01 4.716e-02 5.842e+01 -2.645 0.010478 *
## Cuebottom:Congruencyincongruent 1.630e-02 1.434e-02 1.077e+02 1.136 0.258371
## Cuebottom:Alignmentmisaligned 5.224e-03 1.236e-02 1.623e+02 0.423 0.673007
## Congruencyincongruent:Alignmentmisaligned -4.881e-02 1.387e-02 1.121e+02 -3.520 0.000624 ***
## Cuebottom:Probability2-1 2.721e-01 5.190e-02 3.737e+01 5.244 6.46e-06 ***
## Congruencyincongruent:Probability2-1 -4.404e-02 1.904e-02 3.018e+04 -2.312 0.020775 *
## Alignmentmisaligned:Probability2-1 -3.556e-02 1.832e-02 2.874e+02 -1.941 0.053255 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned -1.675e-03 1.906e-02 5.760e+01 -0.088 0.930246
## Cuebottom:Congruencyincongruent:Probability2-1 7.721e-02 2.697e-02 3.008e+04 2.863 0.004201 **
## Cuebottom:Alignmentmisaligned:Probability2-1 8.364e-02 2.735e-02 8.966e+01 3.059 0.002932 **
## Congruencyincongruent:Alignmentmisaligned:Probability2-1 4.539e-02 2.643e-02 2.998e+04 1.718 0.085863 .
## Cuebottom:Congruencyincongruent:Alignmentmisaligned:Probability2-1 -5.483e-02 3.773e-02 2.956e+04 -1.453 0.146248
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.2.2 Estimated marginal means
3.2.2.1 Estimated marginal means for RT
file_E2_rt_emm <- file.path(folder_lmm, "E2_rt_emm.RData")
if (!file.exists(file_E2_rt_emm)) {
emm_E2_rt <- emmeans(glmm_E2_rt_opt, ~ Cue + Congruency + Alignment + Probability)
} else {
load(file_E2_rt_emm)
}
summary(emm_E2_rt, type = "response") # equivalent to regrid(emm_rt)## Cue Congruency Alignment Probability response SE df asymp.LCL asymp.UCL
## top congruent aligned 0.25 856 39.3 Inf 782 936
## bottom congruent aligned 0.25 745 33.6 Inf 682 813
## top incongruent aligned 0.25 931 43.4 Inf 850 1020
## bottom incongruent aligned 0.25 793 35.8 Inf 725 866
## top congruent misaligned 0.25 908 41.7 Inf 830 994
## bottom congruent misaligned 0.25 762 34.3 Inf 697 832
## top incongruent misaligned 0.25 920 42.6 Inf 840 1007
## bottom incongruent misaligned 0.25 774 34.9 Inf 709 846
## top congruent aligned 0.75 756 34.0 Inf 692 825
## bottom congruent aligned 0.75 863 39.6 Inf 789 944
## top incongruent aligned 0.75 787 35.5 Inf 720 860
## bottom incongruent aligned 0.75 949 44.2 Inf 867 1040
## top congruent misaligned 0.75 774 34.9 Inf 708 845
## bottom congruent misaligned 0.75 926 42.6 Inf 846 1013
## top incongruent misaligned 0.75 785 35.4 Inf 718 857
## bottom incongruent misaligned 0.75 964 44.9 Inf 880 1056
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale# emmip(regrid(emm_E2_rt), Congruency ~ Alignment | Cue + Probability, CIs = TRUE)plot_E2_cf_rt <- summary(emm_E2_rt, type = "response") %>%
as_tibble() %>%
ggplot(aes(y = response, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(Probability ~Cue, switch = "x",
labeller = labeller(Probability = c(`0.25` = "25% cueing top", `0.75` = "75% cueing top"))) +
coord_cartesian(ylim = ylimit_cf_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = "Correct response times (ms)", fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("", "", "**", "***", "", "", "", "", "", "", "*", "*", "", "", "", ""), color = "red", size = 6, nudge_y = 50, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E2_cf_rt.pdf", plot_E2_cf_rt, width = 8, height = 4.8)
plot_E2_cf_rt
3.2.2.2 Composite effects
Composite face effects for top and bottom parts:
emm_E2_rt_cf <- contrast(regrid(emm_E2_rt), interaction = "pairwise", by = c("Cue", "Probability"), infer = TRUE)
emm_E2_rt_cf[1:4]## Congruency_pairwise Alignment_pairwise Cue Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent aligned - misaligned top 0.25 -63.6 21.8 Inf -106.4 -20.823 -2.914 0.0036
## congruent - incongruent aligned - misaligned bottom 0.25 -35.2 10.2 Inf -55.1 -15.210 -3.453 0.0006
## congruent - incongruent aligned - misaligned top 0.75 -20.0 10.0 Inf -39.7 -0.332 -1.993 0.0463
## congruent - incongruent aligned - misaligned bottom 0.75 -48.4 22.7 Inf -92.9 -3.834 -2.129 0.0333
##
## Confidence level used: 0.95emm_E2_rt_con <- contrast(regrid(emm_E2_rt), interaction = "pairwise", by = c("Cue", "Probability", "Alignment"))
summary(emm_E2_rt_con[c(1,2,5,6)], infer = TRUE)## Congruency_pairwise Cue Probability Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent top 0.25 aligned -75.5 16.18 Inf -107.2 -43.8 -4.670 <.0001
## congruent - incongruent bottom 0.25 aligned -47.9 7.93 Inf -63.4 -32.3 -6.032 <.0001
## congruent - incongruent top 0.75 aligned -31.3 7.71 Inf -46.4 -16.2 -4.056 <.0001
## congruent - incongruent bottom 0.75 aligned -86.4 16.50 Inf -118.8 -54.1 -5.239 <.0001
##
## Confidence level used: 0.953.2.2.3 Facilitation and interference
emm_E2_rt_fi <- contrast(regrid(emm_E2_rt), "pairwise", by = c("Cue", "Congruency", "Probability"), infer=TRUE, adjust = "sidak")
emm_E2_rt_fi[1:8]## contrast Cue Congruency Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned top congruent 0.25 -52.23 14.43 Inf -91.56 -12.89 -3.620 0.0023
## aligned - misaligned bottom congruent 0.25 -17.05 7.57 Inf -37.69 3.59 -2.252 0.1787
## aligned - misaligned top incongruent 0.25 11.36 17.29 Inf -35.77 58.50 0.657 0.9967
## aligned - misaligned bottom incongruent 0.25 18.12 8.33 Inf -4.58 40.83 2.177 0.2130
## aligned - misaligned top congruent 0.75 -18.10 7.62 Inf -38.87 2.67 -2.376 0.1318
## aligned - misaligned bottom congruent 0.75 -63.23 14.78 Inf -103.54 -22.92 -4.278 0.0002
## aligned - misaligned top incongruent 0.75 1.92 8.20 Inf -20.44 24.28 0.234 1.0000
## aligned - misaligned bottom incongruent 0.75 -14.84 18.37 Inf -64.93 35.24 -0.808 0.9870
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 8 estimates
## P value adjustment: sidak method for 8 tests# emmip(emm_E2_rt_fi[1:8], ~ Probability | Cue + Congruency, CIs = TRUE, adjust = "sidak") +
# geom_hline(yintercept = 0, linetype = "dashed")plot_E2_cffi_rt <- emm_E2_rt_fi[1:8] %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(Probability ~ Congruency, switch = "x",
labeller = labeller(Probability = c(`0.25` = "25% cueing top", `0.75` = "75% cueing top"))) +
coord_cartesian(ylim = ylimit_cf_fi_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(RT~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E2_fi_rt.pdf", plot_E2_cffi_rt, width = 7, height = 4.55)
plot_E2_cffi_rt
plot_E2_cf_rt_ <- plot_E2_cf_rt +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.6, 0.5),
legend.box = "horizontal")
plot_E2_rt <- ggarrange(plot_E2_cf_rt_, plot_E2_cffi_rt,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E2_rt.pdf", plot_E2_rt, width = 10, height = 7)
plot_E2_rt
3.2.2.4 Comparisons between facilitation and interference
contrast(emm_E2_rt_fi, method = list("faci-inte"=c(1, 1)), by = c("Cue", "Probability"))[1:4] %>%
summary(infer = TRUE)## contrast Cue Probability estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top 0.25 -40.86 23.2 Inf -86.3 4.58 -1.762 0.0780
## faci-inte bottom 0.25 1.08 12.2 Inf -22.9 25.04 0.088 0.9299
## faci-inte top 0.75 -16.18 12.2 Inf -40.2 7.79 -1.323 0.1859
## faci-inte bottom 0.75 -78.07 24.4 Inf -125.9 -30.27 -3.201 0.0014
##
## Confidence level used: 0.954 Experiment 1 and 2
4.1 Responses (d’)
4.1.1 Fitting the generalized mixed models
4.1.1.1 The maximal model
# file_resp_max <- file.path(folder_lmm, "Resp_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_resp_max)) {
# glmm_resp_max <- glmer(
# Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
# (Cue * Congruency * Alignment * SameDifferent | Participant), # Con_Ali_Sam
# family = binomial(link = "probit"),
# data = df_lmm,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_resp_max, file = file_resp_max)
# } else {
# load(file_resp_max)
# }
#
# print(summary(glmm_resp_max), corr = FALSE)4.1.1.2 The zero-correlation-parameter model
file_resp_zcp <- file.path(folder_lmm, "Resp_lmm_zcp.RData")
# fit the zcp model
if (!file.exists(file_resp_zcp)) {
glmm_resp_zcp <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(Cue_C + Con_C + Ali_C + Sam_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam +
Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam || Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_zcp, file = file_resp_zcp)
} else {
load(file_resp_zcp)
}
print(summary(glmm_resp_zcp), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Ali + Con_Sam + Ali_Sam + Cue_Con_Ali + Cue_Con_Sam + Cue_Ali_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 63102.7 63409.5 -31517.3 63034.7 61403
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.7530 -0.6145 0.2261 0.5866 4.5197
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 6.440e-02 2.538e-01
## Participant.1 Cue_C 1.251e-01 3.536e-01
## Participant.2 Con_C 5.088e-03 7.133e-02
## Participant.3 Ali_C 3.884e-02 1.971e-01
## Participant.4 Sam_C 2.193e-01 4.683e-01
## Participant.5 Cue_Con 5.078e-03 7.126e-02
## Participant.6 Cue_Ali 4.189e-02 2.047e-01
## Participant.7 Cue_Sam 7.770e-01 8.815e-01
## Participant.8 Con_Ali 0.000e+00 0.000e+00
## Participant.9 Con_Sam 3.261e-01 5.710e-01
## Participant.10 Ali_Sam 1.306e-14 1.143e-07
## Participant.11 Cue_Con_Ali 0.000e+00 0.000e+00
## Participant.12 Cue_Con_Sam 1.253e+00 1.120e+00
## Participant.13 Cue_Ali_Sam 1.401e-03 3.743e-02
## Participant.14 Con_Ali_Sam 1.067e-01 3.267e-01
## Participant.15 Cue_Con_Ali_Sam 5.275e-02 2.297e-01
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.133017 0.046191 2.880 0.003981 **
## Cue2-1 0.088095 0.046155 1.909 0.056305 .
## Congruency2-1 -0.143440 0.015205 -9.434 < 2e-16 ***
## Alignment2-1 0.056608 0.027580 2.052 0.040126 *
## SameDifferent2-1 -1.366284 0.059928 -22.799 < 2e-16 ***
## Probability0.5 0.042453 0.065205 0.651 0.515005
## Probability0.75 0.030363 0.016168 1.878 0.060389 .
## Cue2-1:Congruency2-1 -0.010243 0.025779 -0.397 0.691134
## Cue2-1:Alignment2-1 -0.103310 0.035394 -2.919 0.003514 **
## Congruency2-1:Alignment2-1 0.127143 0.023738 5.356 8.50e-08 ***
## Cue2-1:SameDifferent2-1 0.318684 0.113248 2.814 0.004892 **
## Congruency2-1:SameDifferent2-1 1.032331 0.075649 13.646 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.010627 0.023866 0.445 0.656103
## Cue2-1:Congruency2-1:Alignment2-1 -0.002245 0.047390 -0.047 0.962220
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.078199 0.148665 -0.526 0.598884
## Cue2-1:Alignment2-1:SameDifferent2-1 0.167988 0.047931 3.505 0.000457 ***
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.573895 0.063344 -9.060 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.632166 0.099337 6.364 1.97e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular4.1.1.3 The reduced model
summary(rePCA(glmm_resp_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
## Standard deviation 1.1196 0.8815 0.5710 0.46832 0.35363 0.32667 0.25378 0.22966 0.20467 0.19708 0.07133 0.07126 0.03743 1.143e-07 0 0
## Proportion of Variance 0.4154 0.2575 0.1081 0.07269 0.04145 0.03537 0.02135 0.01748 0.01388 0.01287 0.00169 0.00168 0.00046 0.000e+00 0 0
## Cumulative Proportion 0.4154 0.6730 0.7811 0.85376 0.89521 0.93058 0.95193 0.96941 0.98329 0.99617 0.99785 0.99954 1.00000 1.000e+00 1 1Con_Ali, Ali_Sam, Cue_Con_Ali, and Cue_Ali_Sam were removed from extended model (glmm_resp_etd) due to that the variances they explained were smaller than 0.1%, making glmm_resp_rdc.
file_resp_rdc <- file.path(folder_lmm, "Resp_lmm_rdc.RData")
# fit the zcp model
# three random effects were removed
if (!file.exists(file_resp_rdc)) {
glmm_resp_rdc <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(Cue_C + Con_C + Ali_C + Sam_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam +
Cue_Con_Sam + Con_Ali_Sam +# Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam || Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_rdc, file = file_resp_rdc)
} else {
load(file_resp_rdc)
}
print(summary(glmm_resp_rdc), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 63094.7 63365.4 -31517.3 63034.7 61407
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.7510 -0.6146 0.2259 0.5868 4.5215
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.064402 0.25378
## Participant.1 Cue_C 0.125050 0.35362
## Participant.2 Con_C 0.005088 0.07133
## Participant.3 Ali_C 0.038835 0.19707
## Participant.4 Sam_C 0.219322 0.46832
## Participant.5 Cue_Con 0.005079 0.07127
## Participant.6 Cue_Ali 0.041875 0.20463
## Participant.7 Cue_Sam 0.777015 0.88148
## Participant.8 Con_Sam 0.326078 0.57103
## Participant.9 Cue_Con_Sam 1.253376 1.11954
## Participant.10 Con_Ali_Sam 0.106723 0.32669
## Participant.11 Cue_Con_Ali_Sam 0.052783 0.22975
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.133020 0.046193 2.880 0.003981 **
## Cue2-1 0.088085 0.046163 1.908 0.056376 .
## Congruency2-1 -0.143434 0.015204 -9.434 < 2e-16 ***
## Alignment2-1 0.056618 0.027582 2.053 0.040104 *
## SameDifferent2-1 -1.366260 0.059919 -22.802 < 2e-16 ***
## Probability0.5 0.042443 0.065206 0.651 0.515106
## Probability0.75 0.030360 0.016168 1.878 0.060405 .
## Cue2-1:Congruency2-1 -0.010254 0.025777 -0.398 0.690775
## Cue2-1:Alignment2-1 -0.103374 0.035371 -2.923 0.003472 **
## Congruency2-1:Alignment2-1 0.127151 0.023736 5.357 8.47e-08 ***
## Cue2-1:SameDifferent2-1 0.318680 0.112984 2.821 0.004794 **
## Congruency2-1:SameDifferent2-1 1.032317 0.075768 13.625 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.010682 0.023847 0.448 0.654191
## Cue2-1:Congruency2-1:Alignment2-1 -0.002169 0.047379 -0.046 0.963483
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.078201 0.148731 -0.526 0.599036
## Cue2-1:Alignment2-1:SameDifferent2-1 0.167813 0.047598 3.526 0.000423 ***
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.573905 0.063347 -9.060 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.632150 0.099361 6.362 1.99e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.1.1.4 The extended model
file_resp_etd <- file.path(folder_lmm, "Resp_lmm_etd.RData")
# fit the etd model
if (!file.exists(file_resp_etd)) {
glmm_resp_etd <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(Cue_C + Con_C + Ali_C + Sam_C +
Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + # Con_Ali + Ali_Sam +
Cue_Con_Sam + Con_Ali_Sam +# Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd, file = glmm_resp_etd)
} else {
load(file_resp_etd)
}
print(summary(glmm_resp_etd), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 63083.0 63949.5 -31445.5 62891.0 61341
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.7764 -0.6110 0.2195 0.5860 5.2220
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.06868 0.26206
## Cue_C 0.12513 0.35374 -0.12
## Con_C 0.00580 0.07616 -0.44 -0.09
## Ali_C 0.03871 0.19674 0.14 -0.02 -0.24
## Sam_C 0.22202 0.47119 -0.07 -0.16 0.59 -0.17
## Cue_Con 0.01401 0.11837 0.02 0.15 0.45 -0.36 0.38
## Cue_Ali 0.04120 0.20297 -0.40 -0.04 0.22 -0.16 0.23 0.06
## Cue_Sam 0.76967 0.87731 0.29 0.03 -0.32 0.17 0.01 -0.49 -0.29
## Con_Sam 0.33708 0.58059 -0.02 -0.22 -0.50 0.01 -0.18 0.02 0.07 0.03
## Cue_Con_Sam 1.24261 1.11473 0.04 -0.07 -0.21 0.09 -0.01 -0.61 -0.32 0.77 0.22
## Con_Ali_Sam 0.10948 0.33088 0.08 0.17 0.24 -0.07 0.27 -0.36 0.06 0.40 -0.46 0.44
## Cue_Con_Ali_Sam 0.19553 0.44219 0.15 -0.02 -0.38 0.02 -0.35 0.02 0.05 0.10 -0.07 -0.45 -0.39
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.190215 0.049826 3.818 0.000135 ***
## Cue2-1 0.086308 0.046234 1.867 0.061935 .
## Congruency2-1 -0.146568 0.015757 -9.302 < 2e-16 ***
## Alignment2-1 0.057107 0.027607 2.069 0.038586 *
## SameDifferent2-1 -1.367728 0.060308 -22.679 < 2e-16 ***
## Probability0.5 -0.068135 0.073251 -0.930 0.352287
## Probability0.75 0.030948 0.016186 1.912 0.055867 .
## Cue2-1:Congruency2-1 -0.008224 0.029046 -0.283 0.777083
## Cue2-1:Alignment2-1 -0.102079 0.035450 -2.880 0.003983 **
## Congruency2-1:Alignment2-1 0.130176 0.024030 5.417 6.06e-08 ***
## Cue2-1:SameDifferent2-1 0.313897 0.112803 2.783 0.005391 **
## Congruency2-1:SameDifferent2-1 1.030473 0.076980 13.386 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.013823 0.024049 0.575 0.565436
## Cue2-1:Congruency2-1:Alignment2-1 -0.008231 0.048046 -0.171 0.863980
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.049411 0.148288 -0.333 0.738973
## Cue2-1:Alignment2-1:SameDifferent2-1 0.171521 0.048081 3.567 0.000361 ***
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.592064 0.064222 -9.219 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.664157 0.112066 5.926 3.10e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_resp_etd))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## Standard deviation 1.3617 0.6534 0.6171 0.45717 0.33683 0.27047 0.22740 0.19526 0.11588 0.09401 0.01508 2.882e-05
## Proportion of Variance 0.5849 0.1347 0.1201 0.06593 0.03579 0.02308 0.01631 0.01203 0.00424 0.00279 0.00007 0.000e+00
## Cumulative Proportion 0.5849 0.7196 0.8398 0.90570 0.94149 0.96456 0.98088 0.99290 0.99714 0.99993 1.00000 1.000e+00Con_C, Cue_Con, Ali_C, and Cue_Ali was removed from extended model.
file_resp_etd1 <- file.path(folder_lmm, "Resp_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_resp_etd1)) {
glmm_resp_etd1 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Sam + Con_Sam + # Cue_Con + Con_Ali + Ali_Sam + Cue_Ali +
Cue_Con_Sam + Con_Ali_Sam +# Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd1, file = glmm_resp_etd1)
} else {
load(file_resp_etd1)
}
print(summary(glmm_resp_etd1), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (Cue_C + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 63245.1 63732.5 -31568.6 63137.1 61383
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.8485 -0.6094 0.2430 0.5779 4.6281
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.06446 0.2539
## Cue_C 0.12309 0.3508 -0.11
## Sam_C 0.21481 0.4635 -0.08 -0.16
## Cue_Sam 0.76338 0.8737 0.28 0.02 0.01
## Con_Sam 0.32412 0.5693 -0.04 -0.22 -0.16 0.03
## Cue_Con_Sam 1.21246 1.1011 0.06 -0.08 0.00 0.77 0.23
## Con_Ali_Sam 0.11567 0.3401 0.11 0.16 0.28 0.41 -0.44 0.45
## Cue_Con_Ali_Sam 0.18204 0.4267 0.13 0.03 -0.39 0.11 -0.05 -0.47 -0.43
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.157667 0.048780 3.232 0.001228 **
## Cue2-1 0.086991 0.045839 1.898 0.057728 .
## Congruency2-1 -0.138649 0.011955 -11.597 < 2e-16 ***
## Alignment2-1 0.040306 0.011744 3.432 0.000599 ***
## SameDifferent2-1 -1.353450 0.059365 -22.799 < 2e-16 ***
## Probability0.5 -0.011632 0.072389 -0.161 0.872343
## Probability0.75 0.030488 0.016134 1.890 0.058796 .
## Cue2-1:Congruency2-1 -0.007521 0.023914 -0.315 0.753140
## Cue2-1:Alignment2-1 -0.087931 0.023489 -3.744 0.000181 ***
## Congruency2-1:Alignment2-1 0.130470 0.023736 5.497 3.87e-08 ***
## Cue2-1:SameDifferent2-1 0.309046 0.112533 2.746 0.006028 **
## Congruency2-1:SameDifferent2-1 1.014579 0.075450 13.447 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.022333 0.023544 0.949 0.342848
## Cue2-1:Congruency2-1:Alignment2-1 -0.015297 0.047475 -0.322 0.747286
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.058703 0.146943 -0.399 0.689527
## Cue2-1:Alignment2-1:SameDifferent2-1 0.143644 0.047082 3.051 0.002281 **
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.592199 0.064522 -9.178 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.678179 0.110018 6.164 7.08e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_resp_etd1))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## Standard deviation 1.3463 0.6445 0.6092 0.44009 0.32770 0.24962 0.19412 2.881e-05
## Proportion of Variance 0.6042 0.1384 0.1237 0.06456 0.03579 0.02077 0.01256 0.000e+00
## Cumulative Proportion 0.6042 0.7426 0.8663 0.93087 0.96667 0.98744 1.00000 1.000e+00Intercept was removed from extended1 model.
file_resp_etd2 <- file.path(folder_lmm, "Resp_lmm_etd2.RData")
# fit the etd2 model
if (!file.exists(file_resp_etd2)) {
glmm_resp_etd2 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(0 + Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Sam + Con_Sam + # Cue_Con + Con_Ali + Ali_Sam + Cue_Ali +
Cue_Con_Sam + Con_Ali_Sam +# Cue_Con_Ali + Cue_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd2, file = glmm_resp_etd2)
} else {
load(file_resp_etd2)
}
print(summary(glmm_resp_etd2), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (0 + Cue_C + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 64871.6 65286.8 -32389.8 64779.6 61391
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3445 -0.6291 0.2780 0.5980 4.0776
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_C 0.1154 0.3397
## Sam_C 0.2102 0.4584 -0.20
## Cue_Sam 0.7150 0.8456 0.08 0.02
## Con_Sam 0.3213 0.5668 -0.22 -0.19 0.03
## Cue_Con_Sam 1.1358 1.0657 -0.10 0.02 0.74 0.23
## Con_Ali_Sam 0.1080 0.3286 0.17 0.30 0.44 -0.47 0.45
## Cue_Con_Ali_Sam 0.1371 0.3703 0.08 -0.41 0.09 -0.05 -0.51 -0.44
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.123252 0.010709 11.509 < 2e-16 ***
## Cue2-1 0.099768 0.044345 2.250 0.024459 *
## Congruency2-1 -0.129109 0.011622 -11.109 < 2e-16 ***
## Alignment2-1 0.037931 0.011558 3.282 0.001031 **
## SameDifferent2-1 -1.314484 0.058587 -22.436 < 2e-16 ***
## Probability0.5 0.043315 0.014521 2.983 0.002855 **
## Probability0.75 0.028661 0.015913 1.801 0.071684 .
## Cue2-1:Congruency2-1 -0.013110 0.023309 -0.562 0.573820
## Cue2-1:Alignment2-1 -0.086384 0.023115 -3.737 0.000186 ***
## Congruency2-1:Alignment2-1 0.126081 0.023204 5.434 5.53e-08 ***
## Cue2-1:SameDifferent2-1 0.285404 0.108480 2.631 0.008515 **
## Congruency2-1:SameDifferent2-1 0.984935 0.074950 13.141 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.025026 0.023195 1.079 0.280613
## Cue2-1:Congruency2-1:Alignment2-1 -0.004488 0.046413 -0.097 0.922973
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.053188 0.141838 -0.375 0.707667
## Cue2-1:Alignment2-1:SameDifferent2-1 0.133972 0.046382 2.888 0.003872 **
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.573698 0.062888 -9.123 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.646349 0.105219 6.143 8.10e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_resp_etd2))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## Standard deviation 1.2954 0.6398 0.5808 0.42799 0.31414 0.19015 8.192e-06
## Proportion of Variance 0.6118 0.1492 0.1230 0.06679 0.03598 0.01318 0.000e+00
## Cumulative Proportion 0.6118 0.7611 0.8841 0.95084 0.98682 1.00000 1.000e+00Con_Ali_Sam was removed from extended1 model.
file_resp_etd3 <- file.path(folder_lmm, "Resp_lmm_etd3.RData")
# fit the etd3 model
if (!file.exists(file_resp_etd3)) {
glmm_resp_etd3 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(0 + Cue_C + Sam_C + # Con_C + Ali_C +
Cue_Sam + Con_Sam + # Cue_Con + Con_Ali + Ali_Sam + Cue_Ali +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd3, file = glmm_resp_etd3)
} else {
load(file_resp_etd3)
}
print(summary(glmm_resp_etd3), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (0 + Cue_C + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 64887.2 65239.2 -32404.6 64809.2 61398
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.0379 -0.6276 0.2795 0.5984 4.4562
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Cue_C 0.1153 0.3396
## Sam_C 0.2089 0.4571 -0.20
## Cue_Sam 0.7157 0.8460 0.08 0.02
## Con_Sam 0.3171 0.5631 -0.22 -0.18 0.03
## Cue_Con_Sam 1.1279 1.0620 -0.10 0.02 0.74 0.24
## Cue_Con_Ali_Sam 0.1336 0.3655 0.08 -0.41 0.10 -0.05 -0.51
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.123177 0.010705 11.507 < 2e-16 ***
## Cue2-1 0.099649 0.044331 2.248 0.024588 *
## Congruency2-1 -0.128751 0.011616 -11.084 < 2e-16 ***
## Alignment2-1 0.038946 0.011548 3.373 0.000745 ***
## SameDifferent2-1 -1.312469 0.058439 -22.459 < 2e-16 ***
## Probability0.5 0.043090 0.014511 2.969 0.002984 **
## Probability0.75 0.028336 0.015907 1.781 0.074848 .
## Cue2-1:Congruency2-1 -0.013659 0.023291 -0.586 0.557572
## Cue2-1:Alignment2-1 -0.087068 0.023090 -3.771 0.000163 ***
## Congruency2-1:Alignment2-1 0.124404 0.023176 5.368 7.98e-08 ***
## Cue2-1:SameDifferent2-1 0.284202 0.108399 2.622 0.008746 **
## Congruency2-1:SameDifferent2-1 0.981504 0.074559 13.164 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.017419 0.023101 0.754 0.450821
## Cue2-1:Congruency2-1:Alignment2-1 -0.002189 0.046186 -0.047 0.962202
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.049675 0.141367 -0.351 0.725299
## Cue2-1:Alignment2-1:SameDifferent2-1 0.136374 0.046292 2.946 0.003219 **
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.553813 0.046301 -11.961 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.652923 0.104533 6.246 4.21e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_resp_etd3))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6]
## Standard deviation 1.2832 0.6208 0.5559 0.42463 0.31154 0
## Proportion of Variance 0.6289 0.1472 0.1180 0.06886 0.03707 0
## Cumulative Proportion 0.6289 0.7761 0.8941 0.96293 1.00000 1Cue_C was removed.
file_resp_etd4 <- file.path(folder_lmm, "Resp_lmm_etd4.RData")
# fit the etd4 model
if (!file.exists(file_resp_etd4)) {
glmm_resp_etd4 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(0 + Sam_C + # Con_C + Ali_C + Cue_C +
Cue_Sam + Con_Sam + # Cue_Con + Con_Ali + Ali_Sam + Cue_Ali +
Cue_Con_Sam + # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam +
Cue_Con_Ali_Sam | Participant),
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd4, file = glmm_resp_etd4)
} else {
load(file_resp_etd4)
}
print(summary(glmm_resp_etd4), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (0 + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam + Cue_Con_Ali_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 65595.0 65892.8 -32764.5 65529.0 61404
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9069 -0.6337 0.2870 0.5997 3.5592
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Sam_C 0.2053 0.4531
## Cue_Sam 0.7240 0.8509 0.01
## Con_Sam 0.3154 0.5616 -0.19 0.02
## Cue_Con_Sam 1.1390 1.0672 0.03 0.70 0.26
## Cue_Con_Ali_Sam 0.1293 0.3595 -0.46 0.13 -0.06 -0.53
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.129522 0.010355 12.508 < 2e-16 ***
## Cue2-1 0.105943 0.012411 8.536 < 2e-16 ***
## Congruency2-1 -0.128304 0.011488 -11.168 < 2e-16 ***
## Alignment2-1 0.038831 0.011471 3.385 0.000711 ***
## SameDifferent2-1 -1.296669 0.057890 -22.399 < 2e-16 ***
## Probability0.5 0.037871 0.014127 2.681 0.007344 **
## Probability0.75 0.014138 0.015141 0.934 0.350402
## Cue2-1:Congruency2-1 -0.013638 0.022974 -0.594 0.552769
## Cue2-1:Alignment2-1 -0.086152 0.022946 -3.755 0.000174 ***
## Congruency2-1:Alignment2-1 0.124053 0.022943 5.407 6.41e-08 ***
## Cue2-1:SameDifferent2-1 0.280842 0.109001 2.577 0.009981 **
## Congruency2-1:SameDifferent2-1 0.971848 0.074277 13.084 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.017533 0.022956 0.764 0.445022
## Cue2-1:Congruency2-1:Alignment2-1 -0.002098 0.045909 -0.046 0.963548
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.047721 0.141789 -0.337 0.736445
## Cue2-1:Alignment2-1:SameDifferent2-1 0.134706 0.046006 2.928 0.003412 **
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.550741 0.046034 -11.964 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.639901 0.103436 6.186 6.15e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularsummary(rePCA(glmm_resp_etd4))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5]
## Standard deviation 1.2764 0.6366 0.5607 0.40497 1.158e-05
## Proportion of Variance 0.6484 0.1613 0.1251 0.06526 0.000e+00
## Cumulative Proportion 0.6484 0.8096 0.9347 1.00000 1.000e+00Cue_Con_Ali_Sam was removed.
file_resp_etd5 <- file.path(folder_lmm, "Resp_lmm_etd5.RData")
# fit the etd5 model
if (!file.exists(file_resp_etd5)) {
glmm_resp_etd5 <- glmer(
Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
(0 + Sam_C + # Con_C + Ali_C + Cue_C +
Cue_Sam + Con_Sam + # Cue_Con + Con_Ali + Ali_Sam + Cue_Ali +
Cue_Con_Sam # Cue_Con_Ali + Cue_Ali_Sam + Con_Ali_Sam + +
| Participant), # Cue_Con_Ali_Sam
family = binomial(link = "probit"),
data = df_lmm,
control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_resp_etd5, file = glmm_resp_etd5)
} else {
load(file_resp_etd5)
}
print(summary(glmm_resp_etd5), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (0 + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam | Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 65596.2 65848.9 -32770.1 65540.2 61409
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8313 -0.6303 0.2892 0.6016 3.5395
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant Sam_C 0.2049 0.4527
## Cue_Sam 0.7207 0.8489 0.01
## Con_Sam 0.3154 0.5616 -0.19 0.02
## Cue_Con_Sam 1.1323 1.0641 0.03 0.71 0.26
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.1294660 0.0103554 12.502 < 2e-16 ***
## Cue2-1 0.1061128 0.0124089 8.551 < 2e-16 ***
## Congruency2-1 -0.1282620 0.0114863 -11.166 < 2e-16 ***
## Alignment2-1 0.0390641 0.0114681 3.406 0.000658 ***
## SameDifferent2-1 -1.2958485 0.0579395 -22.366 < 2e-16 ***
## Probability0.5 0.0377466 0.0141252 2.672 0.007534 **
## Probability0.75 0.0142471 0.0151415 0.941 0.346742
## Cue2-1:Congruency2-1 -0.0134839 0.0229744 -0.587 0.557266
## Cue2-1:Alignment2-1 -0.0866271 0.0229394 -3.776 0.000159 ***
## Congruency2-1:Alignment2-1 0.1243850 0.0229390 5.422 5.88e-08 ***
## Cue2-1:SameDifferent2-1 0.2793811 0.1090565 2.562 0.010413 *
## Congruency2-1:SameDifferent2-1 0.9710948 0.0744207 13.049 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.0151448 0.0229397 0.660 0.509124
## Cue2-1:Congruency2-1:Alignment2-1 0.0004411 0.0458931 0.010 0.992331
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.0459603 0.1419862 -0.324 0.746168
## Cue2-1:Alignment2-1:SameDifferent2-1 0.1389068 0.0459013 3.026 0.002476 **
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.5438443 0.0458885 -11.851 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.6052064 0.0918957 6.586 4.52e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.1.1.5 The optimal model
# compare the extended and reduced model
anova(glmm_resp_etd5, glmm_resp_rdc, refit = FALSE)## Data: df_lmm
## Models:
## glmm_resp_etd5: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
## glmm_resp_etd5: (0 + Sam_C + Cue_Sam + Con_Sam + Cue_Con_Sam | Participant)
## glmm_resp_rdc: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability +
## glmm_resp_rdc: (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam +
## glmm_resp_rdc: Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam ||
## glmm_resp_rdc: Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_resp_etd5 28 65596 65849 -32770 65540
## glmm_resp_rdc 30 63095 63365 -31517 63035 2505.5 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to BIC, the reduced model (glmm_resp_rdc) explained the data better than the extended model (glmm_resp_etd5) and, therefore, the reduced model is used as the optimal model.
glmm_resp_opt <- glmm_resp_rdc
print(summary(glmm_resp_opt), corr = FALSE)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: Resp ~ Cue * Congruency * Alignment * SameDifferent + Probability + (Cue_C + Con_C + Ali_C + Sam_C + Cue_Con + Cue_Ali + Cue_Sam + Con_Sam + Cue_Con_Sam + Con_Ali_Sam + Cue_Con_Ali_Sam || Participant)
## Data: df_lmm
## Control: glmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## AIC BIC logLik deviance df.resid
## 63094.7 63365.4 -31517.3 63034.7 61407
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.7510 -0.6146 0.2259 0.5868 4.5215
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.064402 0.25378
## Participant.1 Cue_C 0.125050 0.35362
## Participant.2 Con_C 0.005088 0.07133
## Participant.3 Ali_C 0.038835 0.19707
## Participant.4 Sam_C 0.219322 0.46832
## Participant.5 Cue_Con 0.005079 0.07127
## Participant.6 Cue_Ali 0.041875 0.20463
## Participant.7 Cue_Sam 0.777015 0.88148
## Participant.8 Con_Sam 0.326078 0.57103
## Participant.9 Cue_Con_Sam 1.253376 1.11954
## Participant.10 Con_Ali_Sam 0.106723 0.32669
## Participant.11 Cue_Con_Ali_Sam 0.052783 0.22975
## Number of obs: 61437, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.133020 0.046193 2.880 0.003981 **
## Cue2-1 0.088085 0.046163 1.908 0.056376 .
## Congruency2-1 -0.143434 0.015204 -9.434 < 2e-16 ***
## Alignment2-1 0.056618 0.027582 2.053 0.040104 *
## SameDifferent2-1 -1.366260 0.059919 -22.802 < 2e-16 ***
## Probability0.5 0.042443 0.065206 0.651 0.515106
## Probability0.75 0.030360 0.016168 1.878 0.060405 .
## Cue2-1:Congruency2-1 -0.010254 0.025777 -0.398 0.690775
## Cue2-1:Alignment2-1 -0.103374 0.035371 -2.923 0.003472 **
## Congruency2-1:Alignment2-1 0.127151 0.023736 5.357 8.47e-08 ***
## Cue2-1:SameDifferent2-1 0.318680 0.112984 2.821 0.004794 **
## Congruency2-1:SameDifferent2-1 1.032317 0.075768 13.625 < 2e-16 ***
## Alignment2-1:SameDifferent2-1 0.010682 0.023847 0.448 0.654191
## Cue2-1:Congruency2-1:Alignment2-1 -0.002169 0.047379 -0.046 0.963483
## Cue2-1:Congruency2-1:SameDifferent2-1 -0.078201 0.148731 -0.526 0.599036
## Cue2-1:Alignment2-1:SameDifferent2-1 0.167813 0.047598 3.526 0.000423 ***
## Congruency2-1:Alignment2-1:SameDifferent2-1 -0.573905 0.063347 -9.060 < 2e-16 ***
## Cue2-1:Congruency2-1:Alignment2-1:SameDifferent2-1 0.632150 0.099361 6.362 1.99e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.1.2 Estimated marginal means
4.1.2.1 Estimated marginal means for hit and false alarm
(emm_resp <- emmeans(glmm_resp_opt, ~ Alignment + Congruency + Cue + SameDifferent))## Alignment Congruency Cue SameDifferent emmean SE df asymp.LCL asymp.UCL
## aligned congruent top same 1.284 0.0705 Inf 1.146 1.422
## misaligned congruent top same 1.142 0.0698 Inf 1.005 1.279
## aligned incongruent top same 0.323 0.0678 Inf 0.190 0.456
## misaligned incongruent top same 0.755 0.0686 Inf 0.620 0.889
## aligned congruent bottom same 1.212 0.0701 Inf 1.075 1.350
## misaligned congruent bottom same 1.042 0.0692 Inf 0.907 1.178
## aligned incongruent bottom same 0.440 0.0679 Inf 0.306 0.573
## misaligned incongruent bottom same 0.525 0.0680 Inf 0.391 0.658
## aligned congruent top different -0.963 0.0689 Inf -1.098 -0.828
## misaligned congruent top different -0.733 0.0683 Inf -0.867 -0.599
## aligned incongruent top different -0.408 0.0679 Inf -0.541 -0.275
## misaligned incongruent top different -0.494 0.0679 Inf -0.627 -0.361
## aligned congruent bottom different -0.603 0.0681 Inf -0.736 -0.470
## misaligned congruent bottom different -0.549 0.0680 Inf -0.683 -0.416
## aligned incongruent bottom different -0.254 0.0677 Inf -0.386 -0.121
## misaligned incongruent bottom different -0.203 0.0677 Inf -0.335 -0.070
##
## Results are averaged over the levels of: Probability
## Results are given on the probit (not the response) scale.
## Confidence level used: 0.954.1.2.2 Estimated marginal means for d’
emm_d <- contrast(emm_resp, method = "pairwise", simple = "SameDifferent")
summary(emm_d[1:8], infer = c(TRUE, FALSE), adjust = "none")## contrast Alignment Congruency Cue estimate SE df asymp.LCL asymp.UCL
## same - different aligned congruent top 2.247 0.103 Inf 2.045 2.449
## same - different misaligned congruent top 1.875 0.102 Inf 1.675 2.076
## same - different aligned incongruent top 0.731 0.100 Inf 0.534 0.928
## same - different misaligned incongruent top 1.249 0.101 Inf 1.051 1.447
## same - different aligned congruent bottom 1.815 0.102 Inf 1.615 2.015
## same - different misaligned congruent bottom 1.592 0.102 Inf 1.393 1.791
## same - different aligned incongruent bottom 0.693 0.100 Inf 0.496 0.890
## same - different misaligned incongruent bottom 0.727 0.101 Inf 0.530 0.924
##
## Results are averaged over the levels of: Probability
## Note: contrasts are still on the probit scale
## Confidence level used: 0.95# emmip(emm_d, Congruency ~ Alignment | Cue, CIs = TRUE)plot_E12_cf_d <- summary(emm_d[1:8], infer = c(TRUE, FALSE), adjust = "sidak") %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(. ~Cue, switch = "both") +
coord_cartesian(ylim = ylimit_cf_d) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = expression("Sensitivity"~italic("d'")), fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("***", "", "", "", "**", "", "", ""), color = "red", size = 6, nudge_y = 0.5, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E12_cf_d.pdf", plot_E12_cf_d, width = 8, height = 4.8)
plot_E12_cf_d
4.1.2.3 Composite effects
Composite face effects for top and bottom parts:
emm_d_cf <- contrast(emm_resp, interaction = "pairwise", by = "Cue")
summary(emm_d_cf[1:2], infer = TRUE)## Alignment_pairwise Congruency_pairwise SameDifferent_pairwise Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned congruent - incongruent same - different top 0.890 0.0814 Inf 0.730 1.049 10.936 <.0001
## aligned - misaligned congruent - incongruent same - different bottom 0.258 0.0796 Inf 0.102 0.414 3.238 0.0012
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.95emm_d_con <- contrast(emm_resp, interaction = "pairwise", by = c("Cue", "Alignment"))
summary(emm_d_con[c(1,3)], infer = TRUE)## Congruency_pairwise SameDifferent_pairwise Cue Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent same - different top aligned 1.52 0.114 Inf 1.29 1.74 13.278 <.0001
## congruent - incongruent same - different bottom aligned 1.12 0.113 Inf 0.90 1.34 9.902 <.0001
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.954.1.2.4 Facilitation and interference
# Sensitivity d'
emm_d_fi <- contrast(emm_resp, interaction = "pairwise", by = c("Cue", "Congruency"), adjust = "sidak")
summary(emm_d_fi[1:4], infer=TRUE)## Alignment_pairwise SameDifferent_pairwise Cue Congruency estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned same - different top congruent 0.3718 0.0561 Inf 0.2321 0.5114 6.631 <.0001
## aligned - misaligned same - different top incongruent -0.5182 0.0500 Inf -0.6429 -0.3936 -10.357 <.0001
## aligned - misaligned same - different bottom congruent 0.2235 0.0542 Inf 0.0884 0.3586 4.122 0.0002
## aligned - misaligned same - different bottom incongruent -0.0343 0.0493 Inf -0.1572 0.0886 -0.696 0.9305
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 4 estimates
## P value adjustment: sidak method for 4 tests# showing the differences between aligned and misaligned (aligned-misaligned)
# emmip(emm_d_fi[1:4], ~ Cue | Congruency, CIs = TRUE, adjust = "sidak") +
# geom_hline(yintercept = 0, linetype = "dashed")plot_E12_cffi_d <- summary(emm_d_fi[1:4], infer=TRUE) %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(. ~ Congruency, switch = "both") +
coord_cartesian(ylim = ylimit_cf_fi_d) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(italic("d'")~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E12_fi_d.pdf", plot_E12_cffi_d, width = 7, height = 4.55)
plot_E12_cffi_d
plot_E12_cf_d_ <- plot_E12_cf_d +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.6, 0.075),
legend.box = "horizontal")
plot_E12_d <- ggarrange(plot_E12_cf_d_, plot_E12_cffi_d,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E12_d.pdf", plot_E12_d, width = 10, height = 4.5)
plot_E12_d
4.1.2.5 Comparisons between facilitation and interference
contrast(emm_d_fi, method = list("faci-inte"=c(1, 1)), by = "Cue")[1:2] %>%
summary(infer = TRUE)## contrast Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top -0.146 0.0684 Inf -0.280 -0.0125 -2.142 0.0322
## faci-inte bottom 0.189 0.0664 Inf 0.059 0.3193 2.849 0.0044
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.954.2 Response times
df_lmm_rt <- df_lmm %>%
filter(isCorrect == 1)
# save(df_lmm_rt, file = file.path("data", "df_lmm_rt.RData"))4.2.1 Fitting the generalized mixed models
with log-transformation. #### The maximal model
# file_rt_max <- file.path(folder_lmm, "rt_lmm_max.RData")
#
# # fit the max model
# if (!file.exists(file_rt_max)) {
# glmm_rt_max <- glmer(
# log(RT) ~ Cue * Congruency * Alignment + Probability +
# (Cue * Congruency * Alignment | Participant),
# family = lognormal(),
# data = df_lmm_rt,
# control = glmerControl(optimizer = "optimx", # calc.derivs = FALSE,
# optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
# )
#
# save(glmm_rt_max, file = file_rt_max)
# } else {
# load(file_rt_max)
# }
#
# print(summary(glmm_rt_max), corr = FALSE)4.2.1.1 The zero-correlation-parameter model
file_rt_zcp <- file.path(folder_lmm, "rt_lmm_zcp.RData")
# fit the zcp1 model
if (!file.exists(file_rt_zcp)) {
glmm_rt_zcp <- lmer(
log(RT) ~ Cue * Congruency * Alignment + Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + Cue_Ali + Con_Ali +
Cue_Con_Ali || Participant),
data = df_lmm_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_rt_zcp, file = file_rt_zcp)
} else {
load(file_rt_zcp)
}
print(summary(glmm_rt_zcp), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Ali + Con_Ali + Cue_Con_Ali || Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37568.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0118 -0.6012 -0.1452 0.4415 9.7535
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 5.531e-02 2.352e-01
## Participant.1 Cue_C 2.039e-02 1.428e-01
## Participant.2 Con_C 6.458e-04 2.541e-02
## Participant.3 Ali_C 7.453e-04 2.730e-02
## Participant.4 Cue_Con 7.533e-04 2.745e-02
## Participant.5 Cue_Ali 8.167e-05 9.037e-03
## Participant.6 Con_Ali 3.866e-11 6.217e-06
## Participant.7 Cue_Con_Ali 5.132e-03 7.164e-02
## Residual 1.334e-01 3.653e-01
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.678e+00 4.171e-02 6.221e+01 160.114 < 2e-16 ***
## Cue2-1 3.909e-02 1.830e-02 6.350e+01 2.136 0.03651 *
## Congruency2-1 3.524e-02 4.819e-03 5.487e+01 7.314 1.17e-09 ***
## Alignment2-1 1.469e-02 4.964e-03 5.570e+01 2.959 0.00452 **
## Probability0.5 8.884e-02 5.897e-02 6.216e+01 1.507 0.13698
## Probability0.75 1.024e-02 5.087e-03 4.364e+04 2.013 0.04407 *
## Cue2-1:Congruency2-1 4.223e-03 7.913e-03 5.078e+01 0.534 0.59592
## Cue2-1:Alignment2-1 -2.254e-03 7.082e-03 3.155e+01 -0.318 0.75234
## Congruency2-1:Alignment2-1 -4.508e-02 6.976e-03 3.982e+04 -6.463 1.04e-10 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.414e-02 1.681e-02 3.807e+01 -0.841 0.40551
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular4.2.1.2 The reduced model
summary(rePCA(glmm_rt_zcp))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## Standard deviation 0.6438 0.3909 0.19612 0.07514 0.07474 0.06957 0.02474 1.702e-05
## Proportion of Variance 0.6660 0.2455 0.06179 0.00907 0.00897 0.00778 0.00098 0.000e+00
## Cumulative Proportion 0.6660 0.9114 0.97320 0.98227 0.99124 0.99902 1.00000 1.000e+00Con_Ali, and Cue_Ali were removed from extended model (glmm_rt_zcp) due to that the variances they explained were smaller than 0.1%, making glmm_rt_rdc.
file_rt_rdc <- file.path(folder_lmm, "rt_lmm_rdc.RData")
# fit the zcp model
# three random effects were removed
if (!file.exists(file_rt_rdc)) {
glmm_rt_rdc <- lmer(
log(RT) ~ Cue * Congruency * Alignment + Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + # Con_Ali + Cue_Ali +
Cue_Con_Ali || Participant),
data = df_lmm_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_rt_rdc, file = file_rt_rdc)
} else {
load(file_rt_rdc)
}
print(summary(glmm_rt_rdc), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Con_Ali || Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37568.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0114 -0.6010 -0.1454 0.4413 9.7530
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0553065 0.23517
## Participant.1 Cue_C 0.0203864 0.14278
## Participant.2 Con_C 0.0006454 0.02540
## Participant.3 Ali_C 0.0007437 0.02727
## Participant.4 Cue_Con 0.0007531 0.02744
## Participant.5 Cue_Con_Ali 0.0051144 0.07151
## Residual 0.1334233 0.36527
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.678e+00 4.171e-02 6.221e+01 160.114 < 2e-16 ***
## Cue2-1 3.910e-02 1.830e-02 6.350e+01 2.136 0.03651 *
## Congruency2-1 3.524e-02 4.818e-03 5.488e+01 7.315 1.16e-09 ***
## Alignment2-1 1.468e-02 4.961e-03 5.586e+01 2.959 0.00452 **
## Probability0.5 8.884e-02 5.897e-02 6.216e+01 1.507 0.13700
## Probability0.75 1.024e-02 5.087e-03 4.369e+04 2.013 0.04411 *
## Cue2-1:Congruency2-1 4.227e-03 7.913e-03 5.079e+01 0.534 0.59555
## Cue2-1:Alignment2-1 -2.343e-03 6.978e-03 4.357e+04 -0.336 0.73703
## Congruency2-1:Alignment2-1 -4.510e-02 6.975e-03 4.236e+04 -6.465 1.02e-10 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.414e-02 1.680e-02 3.814e+01 -0.841 0.40538
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.2.1.3 The extended model
file_rt_etd <- file.path(folder_lmm, "rt_lmm_etd.RData")
# fit the etd model
if (!file.exists(file_rt_etd)) {
glmm_rt_etd <- lmer(
log(RT) ~ Cue * Congruency * Alignment + Probability +
(Cue_C + Con_C + Ali_C +
Cue_Con + # Con_Ali + Cue_Ali +
Cue_Con_Ali | Participant),
data = df_lmm_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_rt_etd, file = glmm_rt_etd)
} else {
load(file_rt_etd)
}
print(summary(glmm_rt_etd), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Con_Ali | Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37540.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0149 -0.6012 -0.1444 0.4431 9.7665
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0550740 0.23468
## Cue_C 0.0203309 0.14259 -0.07
## Con_C 0.0006861 0.02619 -0.14 0.45
## Ali_C 0.0008223 0.02868 -0.08 -0.12 0.31
## Cue_Con 0.0011893 0.03449 0.17 0.24 0.03 -0.72
## Cue_Con_Ali 0.0054717 0.07397 -0.72 0.11 -0.37 -0.10 -0.37
## Residual 0.1333885 0.36522
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.672e+00 3.986e-02 6.803e+01 167.402 < 2e-16 ***
## Cue2-1 3.912e-02 1.828e-02 6.342e+01 2.140 0.03618 *
## Congruency2-1 3.621e-02 4.867e-03 5.542e+01 7.440 6.88e-10 ***
## Alignment2-1 1.471e-02 5.075e-03 5.567e+01 2.898 0.00537 **
## Probability0.5 1.002e-01 5.378e-02 6.300e+01 1.863 0.06707 .
## Probability0.75 1.010e-02 5.085e-03 4.336e+04 1.986 0.04707 *
## Cue2-1:Congruency2-1 4.786e-03 8.328e-03 5.356e+01 0.575 0.56789
## Cue2-1:Alignment2-1 -2.922e-03 6.971e-03 4.343e+04 -0.419 0.67507
## Congruency2-1:Alignment2-1 -4.461e-02 6.965e-03 4.312e+04 -6.404 1.53e-10 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.339e-02 1.693e-02 5.914e+01 -0.791 0.43230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.0169721 (tol = 0.002, component 1)file_rt_etd1 <- file.path(folder_lmm, "rt_lmm_etd1.RData")
# fit the etd1 model
if (!file.exists(file_rt_etd1)) {
ss <- getME(glmm_rt_etd, c("theta","fixef"))
glmm_rt_etd1 <- update(
glmm_rt_etd, start=ss,
control=lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
} else {
load(file_rt_etd1)
}
print(summary(glmm_rt_etd1), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Con_Ali | Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37540.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0149 -0.6012 -0.1445 0.4431 9.7665
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0550740 0.23468
## Cue_C 0.0203296 0.14258 -0.07
## Con_C 0.0006850 0.02617 -0.14 0.45
## Ali_C 0.0008217 0.02867 -0.08 -0.12 0.31
## Cue_Con 0.0011887 0.03448 0.17 0.24 0.03 -0.72
## Cue_Con_Ali 0.0054717 0.07397 -0.72 0.11 -0.37 -0.10 -0.37
## Residual 0.1333887 0.36522
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.672e+00 3.986e-02 6.803e+01 167.400 < 2e-16 ***
## Cue2-1 3.912e-02 1.828e-02 6.343e+01 2.140 0.03617 *
## Congruency2-1 3.621e-02 4.865e-03 5.547e+01 7.442 6.78e-10 ***
## Alignment2-1 1.470e-02 5.074e-03 5.570e+01 2.898 0.00536 **
## Probability0.5 1.002e-01 5.378e-02 6.299e+01 1.863 0.06711 .
## Probability0.75 1.010e-02 5.085e-03 4.336e+04 1.986 0.04707 *
## Cue2-1:Congruency2-1 4.786e-03 8.327e-03 5.357e+01 0.575 0.56791
## Cue2-1:Alignment2-1 -2.922e-03 6.971e-03 4.343e+04 -0.419 0.67505
## Congruency2-1:Alignment2-1 -4.461e-02 6.965e-03 4.312e+04 -6.404 1.53e-10 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.339e-02 1.693e-02 5.914e+01 -0.791 0.43222
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (optimx) convergence code: 1
## Model failed to converge with max|grad| = 0.0167706 (tol = 0.002, component 1)summary(rePCA(glmm_rt_etd1))## $Participant
## Importance of components:
## [,1] [,2] [,3] [,4] [,5] [,6]
## Standard deviation 0.6608 0.3912 0.15145 0.11135 0.03757 0.0008193
## Proportion of Variance 0.6970 0.2443 0.03661 0.01979 0.00225 0.0000000
## Cumulative Proportion 0.6970 0.9414 0.97796 0.99775 1.00000 1.0000000Con_C and Ali_C were removed from extended model (glmm_resp_etd1) due to that the variances they explained were smaller than 1%, making glmm_resp_etd2.
file_rt_etd2 <- file.path(folder_lmm, "rt_lmm_etd2.RData")
# fit the etd2 model
if (!file.exists(file_rt_etd2)) {
glmm_rt_etd2 <- lmer(
log(RT) ~ Cue * Congruency * Alignment + Probability +
(Cue_C + # Con_C + Ali_C +
Cue_Con + # Con_Ali + Cue_Ali +
Cue_Con_Ali | Participant),
data = df_lmm_rt,
control = lmerControl(optimizer = "optimx", # calc.derivs = FALSE,
optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
)
# save(glmm_rt_etd2, file = file_rt_etd2)
} else {
load(file_rt_etd2)
}
print(summary(glmm_rt_etd2), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Cue_Con + Cue_Con_Ali | Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37587.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9925 -0.6004 -0.1446 0.4413 9.7582
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0552105 0.23497
## Cue_C 0.0203947 0.14281 -0.07
## Cue_Con 0.0007303 0.02702 0.14 0.27
## Cue_Con_Ali 0.0048203 0.06943 -0.77 0.09 -0.49
## Residual 0.1337601 0.36573
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.674e+00 4.004e-02 6.743e+01 166.698 < 2e-16 ***
## Cue2-1 3.916e-02 1.830e-02 6.344e+01 2.139 0.0363 *
## Congruency2-1 3.514e-02 3.508e-03 3.876e+04 10.017 < 2e-16 ***
## Alignment2-1 1.379e-02 3.483e-03 4.367e+04 3.961 7.48e-05 ***
## Probability0.5 9.634e-02 5.422e-02 6.218e+01 1.777 0.0805 .
## Probability0.75 1.030e-02 5.092e-03 4.368e+04 2.023 0.0431 *
## Cue2-1:Congruency2-1 4.982e-03 7.858e-03 4.983e+01 0.634 0.5290
## Cue2-1:Alignment2-1 -2.427e-03 6.965e-03 4.418e+04 -0.348 0.7275
## Congruency2-1:Alignment2-1 -4.614e-02 6.968e-03 4.154e+04 -6.622 3.58e-11 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.371e-02 1.663e-02 3.757e+01 -0.824 0.4149
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.2.1.4 The optimal model
# compare the extended and reduced model
anova(glmm_rt_etd2, glmm_rt_rdc, refit = FALSE)## Data: df_lmm_rt
## Models:
## glmm_rt_rdc: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C +
## glmm_rt_rdc: Con_C + Ali_C + Cue_Con + Cue_Con_Ali || Participant)
## glmm_rt_etd2: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C +
## glmm_rt_etd2: Cue_Con + Cue_Con_Ali | Participant)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## glmm_rt_rdc 17 37602 37750 -18784 37568
## glmm_rt_etd2 21 37629 37812 -18794 37587 0 4 1According to BIC, the reduced model (glmm_resp_rdc) explained the data better than the extended model (glmm_resp_etd2) and, therefore, the reduced model is used as the optimal model.
glmm_rt_opt <- glmm_rt_rdc
print(summary(glmm_rt_opt), corr = FALSE)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: log(RT) ~ Cue * Congruency * Alignment + Probability + (Cue_C + Con_C + Ali_C + Cue_Con + Cue_Con_Ali || Participant)
## Data: df_lmm_rt
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))
##
## REML criterion at convergence: 37568.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0114 -0.6010 -0.1454 0.4413 9.7530
##
## Random effects:
## Groups Name Variance Std.Dev.
## Participant (Intercept) 0.0553065 0.23517
## Participant.1 Cue_C 0.0203864 0.14278
## Participant.2 Con_C 0.0006454 0.02540
## Participant.3 Ali_C 0.0007437 0.02727
## Participant.4 Cue_Con 0.0007531 0.02744
## Participant.5 Cue_Con_Ali 0.0051144 0.07151
## Residual 0.1334233 0.36527
## Number of obs: 44710, groups: Participant, 64
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.678e+00 4.171e-02 6.221e+01 160.114 < 2e-16 ***
## Cue2-1 3.910e-02 1.830e-02 6.350e+01 2.136 0.03651 *
## Congruency2-1 3.524e-02 4.818e-03 5.488e+01 7.315 1.16e-09 ***
## Alignment2-1 1.468e-02 4.961e-03 5.586e+01 2.959 0.00452 **
## Probability0.5 8.884e-02 5.897e-02 6.216e+01 1.507 0.13700
## Probability0.75 1.024e-02 5.087e-03 4.369e+04 2.013 0.04411 *
## Cue2-1:Congruency2-1 4.227e-03 7.913e-03 5.079e+01 0.534 0.59555
## Cue2-1:Alignment2-1 -2.343e-03 6.978e-03 4.357e+04 -0.336 0.73703
## Congruency2-1:Alignment2-1 -4.510e-02 6.975e-03 4.236e+04 -6.465 1.02e-10 ***
## Cue2-1:Congruency2-1:Alignment2-1 -1.414e-02 1.680e-02 3.814e+01 -0.841 0.40538
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 14.2.2 Estimated marginal means
4.2.2.1 Estimated marginal means for RT
file_rt_emm <- file.path(folder_lmm, "rt_emm.RData")
if (!file.exists(file_rt_emm)) {
emm_rt <- emmeans(glmm_rt_opt, ~ Cue + Congruency + Alignment)
} else {
load(file_rt_emm)
}
summary(emm_rt, type = "response") # equivalent to regrid(emm_rt)## Cue Congruency Alignment response SE df asymp.LCL asymp.UCL
## top congruent aligned 778 25.5 Inf 730 830
## bottom congruent aligned 806 26.4 Inf 756 859
## top incongruent aligned 820 26.9 Inf 769 874
## bottom incongruent aligned 859 28.2 Inf 805 916
## top congruent misaligned 806 26.4 Inf 756 859
## bottom congruent misaligned 838 27.4 Inf 786 894
## top incongruent misaligned 817 26.8 Inf 767 872
## bottom incongruent misaligned 848 27.8 Inf 795 904
##
## Results are averaged over the levels of: Probability
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale# emmip(regrid(emm_rt), Congruency ~ Alignment | Cue, CIs = TRUE)plot_E12_cf_rt <- summary(emm_rt, type = "response") %>%
as_tibble() %>%
ggplot(aes(y = response, x = Alignment, color = Congruency, group = Congruency)) +
geom_point(position = position_dodge(width = 0.1), size = 2) +
geom_line(aes(linetype = Congruency), position = position_dodge(width = 0.1),
size = 0.8) +
scale_linetype_manual(values=c("solid", "dashed"))+
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6, position = position_dodge(width = 0.1),
show.legend = F) +
facet_grid(. ~Cue, switch = "both") +
coord_cartesian(ylim = ylimit_cf_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Target half", y = "Correct response times (ms)", fill = "Congruency") + # set the names for main, x and y axises
geom_text(label = c("", "", "***", "***", "", "", "", ""), color = "red", size = 6, nudge_y = 50, nudge_x = 0.5) + # add starts to the significant columns
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "right",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
)
# ggsave(filename = "E12_cf_rt.pdf", plot_E12_cf_rt, width = 8, height = 4.8)
plot_E12_cf_rt
4.2.2.2 Composite effects
Composite face effects for top and bottom parts:
emm_rt_cf <- contrast(regrid(emm_rt), interaction = "pairwise", by = "Cue", infer = TRUE)
emm_rt_cf[1:2]## Congruency_pairwise Alignment_pairwise Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent aligned - misaligned top -30.2 8.76 Inf -47.4 -13.0 -3.447 0.0006
## congruent - incongruent aligned - misaligned bottom -43.3 9.37 Inf -61.6 -24.9 -4.616 <.0001
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.95# emmip(emm_rt_cf[1:2], ~ Cue , CIs = TRUE) +
# geom_hline(yintercept = 0, linetype = "dashed")emm_rt_con <- contrast(regrid(emm_rt), interaction = "pairwise", by = c("Cue", "Alignment"))
summary(emm_rt_con[c(1,2)], infer = TRUE)## Congruency_pairwise Cue Alignment estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## congruent - incongruent top aligned -41.7 6.75 Inf -54.9 -28.4 -6.168 <.0001
## congruent - incongruent bottom aligned -52.8 7.19 Inf -66.9 -38.7 -7.344 <.0001
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.954.2.2.3 Facilitation and interference
emm_rt_fi <- contrast(regrid(emm_rt), "pairwise", by = c("Cue", "Congruency"), infer=TRUE, adjust = "sidak")
emm_rt_fi[1:4]## contrast Cue Congruency estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## aligned - misaligned top congruent -27.62 6.22 Inf -43.11 -12.1 -4.440 <.0001
## aligned - misaligned bottom congruent -32.54 6.59 Inf -48.96 -16.1 -4.935 <.0001
## aligned - misaligned top incongruent 2.59 6.85 Inf -14.48 19.7 0.378 0.9925
## aligned - misaligned bottom incongruent 10.73 7.32 Inf -7.49 28.9 1.466 0.4594
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 4 estimates
## P value adjustment: sidak method for 4 tests# emmip(emm_rt_fi[1:4], ~ Cue | Congruency, CIs = TRUE, adjust = "sidak") +
# geom_hline(yintercept = 0, linetype = "dashed")plot_E12_cffi_rt <- emm_rt_fi[1:4] %>%
as_tibble() %>%
ggplot(aes(y = estimate, x = Cue, color = Congruency)) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = asymp.LCL, ymax = asymp.UCL), size=1.5, width=0,
alpha = .6) +
geom_hline(yintercept = 0, linetype = "dashed") +
facet_grid(. ~ Congruency, switch = "both") +
coord_cartesian(ylim = ylimit_cf_fi_rt) + # set the limit for y axis c(0, 1100)
labs(x = "Congruency", y = expression(RT~"(aligned-misaligned)")) + # set the names for main, x and y axises
theme_bw() +
theme(
text = element_text(size = 10),
axis.title = element_text(size = 16),
axis.text = element_text(size = 14), # the size of the texts in plot
# axis.text.x = element_text(angle = 45, vjust = 0.5),
legend.title=element_text(size=15),
legend.text=element_text(size=14),
legend.position = "none",
legend.key.width = unit(1.2, "cm"),
plot.title = element_text(lineheight=.8, face="bold", size = 17),
panel.border = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
axis.line.x = element_line(colour = 'black', size=0.5, linetype='solid'),
axis.line.y = element_line(colour = 'black', size=0.5, linetype='solid'),
# remove the facet background color
strip.text = element_text(face="bold", size=14, lineheight=5.0),
strip.background = element_rect(fill="white", colour="white", size=1),
strip.placement = "outside"
) +
NULL
# ggsave(filename = "E12_fi_rt.pdf", plot_E12_cffi_rt, width = 7, height = 4.55)
plot_E12_cffi_rt
plot_E12_cf_rt_ <- plot_E12_cf_rt +
guides(color = guide_legend(nrow = 1, title.position = "left"),
linetype = guide_legend(nrow = 1, title.position = "left")) +
theme(legend.position = c(0.55, 0.075),
legend.box = "horizontal")
plot_E12_rt <- ggarrange(plot_E12_cf_rt_, plot_E12_cffi_rt,
labels = c("A", "B"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 1)
# ggsave(filename = "E12_rt.pdf", plot_E12_rt, width = 10, height = 4.5)
plot_E12_rt
4.2.2.4 Comparisons between facilitation and interference
contrast(emm_rt_fi, method = list("faci-inte"=c(1, 1)), by = "Cue")[1:2] %>%
summary(infer = TRUE)## contrast Cue estimate SE df asymp.LCL asymp.UCL z.ratio p.value
## faci-inte top -25.0 9.72 Inf -44.1 -5.97 -2.574 0.0100
## faci-inte bottom -21.8 10.30 Inf -42.0 -1.62 -2.118 0.0342
##
## Results are averaged over the levels of: Probability
## Confidence level used: 0.955 Plots for publication
5.1 Experiment 1
plot_E1 <- ggarrange(plot_E1_cf_d_, plot_E1_cffi_d,
plot_E1_cf_rt_, plot_E1_cffi_rt,
labels = c("A", "B", "C", "D"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 2, ncol = 2)
# ggsave(filename = "E1.pdf", plot_E1, width = 10, height = 9)
plot_E1
5.2 Experiment 2
plot_E2 <- ggarrange(plot_E2_cf_d_, plot_E2_cffi_d,
plot_E2_cf_rt_, plot_E2_cffi_rt,
labels = c("A", "B", "C", "D"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 2, ncol = 2)
# ggsave(filename = "E2.pdf", plot_E2, width = 10, height = 14)
plot_E2
5.3 Experiment 1&2
plot_E12 <- ggarrange(plot_E12_cf_d_, plot_E12_cffi_d,
plot_E12_cf_rt_, plot_E12_cffi_rt,
labels = c("A", "B", "C", "D"),
font.label = (list(size = 20)),
widths = c(1.5, 1),
nrow = 2, ncol = 2)
# ggsave(filename = "E12.pdf", plot_E12, width = 10, height = 9)
plot_E12
Session information
sessionInfo()## R version 4.0.5 (2021-03-31)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggpubr_0.4.0 emmeans_1.6.3 optimx_2020-4.2 lmerTest_3.1-3 lme4_1.1-26 Matrix_1.3-2 readxl_1.3.1 forcats_0.5.1 stringr_1.4.0 dplyr_1.0.5 purrr_0.3.4 readr_1.4.0 tidyr_1.1.3 tibble_3.1.1 ggplot2_3.3.5 tidyverse_1.3.1
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-152 fs_1.5.0 lubridate_1.7.10 httr_1.4.2 numDeriv_2016.8-1.1 tools_4.0.5 backports_1.2.1 utf8_1.2.1 R6_2.5.0 DBI_1.1.0 colorspace_1.4-1 withr_2.4.2 tidyselect_1.1.0 curl_4.3.1 compiler_4.0.5 cli_2.5.0 rvest_1.0.0 xml2_1.3.2 labeling_0.4.2 scales_1.1.1 mvtnorm_1.1-1 digest_0.6.27 foreign_0.8-81 minqa_1.2.4 rmarkdown_2.7 rio_0.5.26 pkgconfig_2.0.3 htmltools_0.5.1.1 highr_0.9 dbplyr_2.1.1 rlang_0.4.11 rstudioapi_0.13 farver_2.0.3 generics_0.1.0 jsonlite_1.7.2 zip_2.1.1 car_3.0-10 magrittr_2.0.1 Rcpp_1.0.6 munsell_0.5.0 fansi_0.4.2 abind_1.4-5 lifecycle_1.0.0 stringi_1.6.1 yaml_2.2.1 carData_3.0-4 MASS_7.3-53.1 plyr_1.8.6 grid_4.0.5 crayon_1.4.1 lattice_0.20-41 cowplot_1.1.1 haven_2.3.1 splines_4.0.5 hms_1.0.0 knitr_1.33 pillar_1.6.0 uuid_0.1-4 boot_1.3-27 estimability_1.3 ggsignif_0.6.1 reprex_2.0.0 glue_1.4.2 evaluate_0.14 data.table_1.14.0 modelr_0.1.8 vctrs_0.3.8 nloptr_1.2.2.2 cellranger_1.1.0 gtable_0.3.0 assertthat_0.2.1 xfun_0.22 openxlsx_4.2.3 xtable_1.8-4
## [75] broom_0.7.6 coda_0.19-4 rstatix_0.7.0 statmod_1.4.35 ellipsis_0.3.2 xaringanExtra_0.4.0